Models

Models currently supported by StatsForecast

StatsForecast offers a wide variety of models grouped in the following categories:

• Auto Forecast: Automatic forecasting tools search for the best parameters and select the best possible model for a series of time series. These tools are useful for large collections of univariate time series. Includes automatic versions of: Arima, ETS, Theta, CES.

• Exponential Smoothing: Uses a weighted average of all past observations where the weights decrease exponentially into the past. Suitable for data with clear trend and/or seasonality. Use the SimpleExponential family for data with no clear trend or seasonality. Examples: SES, Holt’s Winters, SSO.

• Benchmark models: classical models for establishing baselines. Examples: Mean, Naive, Random Walk

• Intermittent or Sparse models: suited for series with very few non-zero observations. Examples: CROSTON, ADIDA, IMAPA

• Multiple Seasonalities: suited for signals with more than one clear seasonality. Useful for low-frequency data like electricity and logs. Examples: MSTL and TBATS.

• Theta Models: fit two theta lines to a deseasonalized time series, using different techniques to obtain and combine the two theta lines to produce the final forecasts. Examples: Theta, DynamicTheta

• GARCH Model: suited for modeling time series that exhibit non-constant volatility over time. Commonly used in finance to model stock prices, exchange rates, interest rates, and other financial instruments. The ARCH model is a particular case of GARCH.

Automatic Forecasting

AutoARIMA

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AutoARIMA

 AutoARIMA (d:Optional[int]=None, D:Optional[int]=None, max_p:int=5,
            max_q:int=5, max_P:int=2, max_Q:int=2, max_order:int=5,
            max_d:int=2, max_D:int=1, start_p:int=2, start_q:int=2,
            start_P:int=1, start_Q:int=1, stationary:bool=False,
            seasonal:bool=True, ic:str='aicc', stepwise:bool=True,
            nmodels:int=94, trace:bool=False,
            approximation:Optional[bool]=False, method:Optional[str]=None,
            truncate:Optional[bool]=None, test:str='kpss',
            test_kwargs:Optional[str]=None, seasonal_test:str='seas',
            seasonal_test_kwargs:Optional[Dict]=None,
            allowdrift:bool=True, allowmean:bool=True,
            blambda:Optional[float]=None, biasadj:bool=False,
            season_length:int=1, alias:str='AutoARIMA', prediction_interva
            ls:Optional[statsforecast.utils.ConformalIntervals]=None)

*AutoARIMA model.

Automatically selects the best ARIMA (AutoRegressive Integrated Moving Average) model using an information criterion. Default is Akaike Information Criterion (AICc).*

	Type	Default	Details
d	Optional	None	Order of first-differencing.
D	Optional	None	Order of seasonal-differencing.
max_p	int	5	Max autorregresives p.
max_q	int	5	Max moving averages q.
max_P	int	2	Max seasonal autorregresives P.
max_Q	int	2	Max seasonal moving averages Q.
max_order	int	5	Max p+q+P+Q value if not stepwise selection.
max_d	int	2	Max non-seasonal differences.
max_D	int	1	Max seasonal differences.
start_p	int	2	Starting value of p in stepwise procedure.
start_q	int	2	Starting value of q in stepwise procedure.
start_P	int	1	Starting value of P in stepwise procedure.
start_Q	int	1	Starting value of Q in stepwise procedure.
stationary	bool	False	If True, restricts search to stationary models.
seasonal	bool	True	If False, restricts search to non-seasonal models.
ic	str	aicc	Information criterion to be used in model selection.
stepwise	bool	True	If True, will do stepwise selection (faster).
nmodels	int	94	Number of models considered in stepwise search.
trace	bool	False	If True, the searched ARIMA models is reported.
approximation	Optional	False	If True, conditional sums-of-squares estimation, final MLE.
method	Optional	None	Fitting method between maximum likelihood or sums-of-squares.
truncate	Optional	None	Observations truncated series used in model selection.
test	str	kpss	Unit root test to use. See ndiffs for details.
test_kwargs	Optional	None	Unit root test additional arguments.
seasonal_test	str	seas	Selection method for seasonal differences.
seasonal_test_kwargs	Optional	None	Seasonal unit root test arguments.
allowdrift	bool	True	If True, drift models terms considered.
allowmean	bool	True	If True, non-zero mean models considered.
blambda	Optional	None	Box-Cox transformation parameter.
biasadj	bool	False	Use adjusted back-transformed mean Box-Cox.
season_length	int	1	Number of observations per unit of time. Ex: 24 Hourly data.
alias	str	AutoARIMA	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

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AutoARIMA.fit

 AutoARIMA.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the AutoARIMA model.

Fit an AutoARIMA to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			AutoARIMA fitted model.

---

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AutoARIMA.predict

 AutoARIMA.predict (h:int, X:Optional[numpy.ndarray]=None,
                    level:Optional[List[int]]=None)

Predict with fitted AutoArima.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

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AutoARIMA.predict_in_sample

 AutoARIMA.predict_in_sample (level:Optional[List[int]]=None)

Access fitted AutoArima insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

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AutoARIMA.forecast

 AutoARIMA.forecast (y:numpy.ndarray, h:int,
                     X:Optional[numpy.ndarray]=None,
                     X_future:Optional[numpy.ndarray]=None,
                     level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient AutoARIMA predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenpus of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x) optional exogenous.
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

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AutoARIMA.forward

 AutoARIMA.forward (y:numpy.ndarray, h:int,
                    X:Optional[numpy.ndarray]=None,
                    X_future:Optional[numpy.ndarray]=None,
                    level:Optional[List[int]]=None, fitted:bool=False)

Apply fitted ARIMA model to a new time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import AutoARIMA
from statsforecast.utils import AirPassengers as ap

# AutoARIMA's usage example
arima = AutoARIMA(season_length=4)
arima = arima.fit(y=ap)
y_hat_dict = arima.predict(h=4, level=[80])
y_hat_dict

AutoETS

---

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AutoETS

 AutoETS (season_length:int=1, model:str='ZZZ',
          damped:Optional[bool]=None, phi:Optional[float]=None,
          alias:str='AutoETS', prediction_intervals:Optional[statsforecast
          .utils.ConformalIntervals]=None)

*Automatic Exponential Smoothing model.

Automatically selects the best ETS (Error, Trend, Seasonality) model using an information criterion. Default is Akaike Information Criterion (AICc), while particular models are estimated using maximum likelihood. The state-space equations can be determined based on their $M$ multiplicative, $A$ additive, $Z$ optimized or $N$ ommited components. The model string parameter defines the ETS equations: E in [$M, A, Z$], T in [$N, A, M, Z$], and S in [$N, A, M, Z$].

For example when model=‘ANN’ (additive error, no trend, and no seasonality), ETS will explore only a simple exponential smoothing.

If the component is selected as ‘Z’, it operates as a placeholder to ask the AutoETS model to figure out the best parameter.*

	Type	Default	Details
season_length	int	1	Number of observations per unit of time. Ex: 24 Hourly data.
model	str	ZZZ	Controlling state-space-equations.
damped	Optional	None	A parameter that ‘dampens’ the trend.
phi	Optional	None	Smoothing parameter for trend damping. Only used when damped=True.
alias	str	AutoETS	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

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AutoETS.fit

 AutoETS.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the Exponential Smoothing model.

Fit an Exponential Smoothing model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			Exponential Smoothing fitted model.

---

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AutoETS.predict

 AutoETS.predict (h:int, X:Optional[numpy.ndarray]=None,
                  level:Optional[List[int]]=None)

Predict with fitted Exponential Smoothing.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenpus of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

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AutoETS.predict_in_sample

 AutoETS.predict_in_sample (level:Optional[List[int]]=None)

Access fitted Exponential Smoothing insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

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AutoETS.forecast

 AutoETS.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                   X_future:Optional[numpy.ndarray]=None,
                   level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient Exponential Smoothing predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenpus of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

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AutoETS.forward

 AutoETS.forward (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                  X_future:Optional[numpy.ndarray]=None,
                  level:Optional[List[int]]=None, fitted:bool=False)

Apply fitted Exponential Smoothing model to a new time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenpus of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import AutoETS
from statsforecast.utils import AirPassengers as ap

# AutoETS' usage example
# Multiplicative trend, optimal error and seasonality
autoets = AutoETS(model='ZMZ', season_length=4)
autoets = autoets.fit(y=ap)
y_hat_dict = autoets.predict(h=4)
y_hat_dict

AutoCES

---

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AutoCES

 AutoCES (season_length:int=1, model:str='Z', alias:str='CES', prediction_
          intervals:Optional[statsforecast.utils.ConformalIntervals]=None)

*Complex Exponential Smoothing model.

Automatically selects the best Complex Exponential Smoothing model using an information criterion. Default is Akaike Information Criterion (AICc), while particular models are estimated using maximum likelihood. The state-space equations can be determined based on their $S$ simple, $P$ parial, $Z$ optimized or $N$ ommited components. The model string parameter defines the kind of CES model: $N$ for simple CES (withous seasonality), $S$ for simple seasonality (lagged CES), $P$ for partial seasonality (without complex part), $F$ for full seasonality (lagged CES with real and complex seasonal parts).

If the component is selected as ‘Z’, it operates as a placeholder to ask the AutoCES model to figure out the best parameter.*

	Type	Default	Details
season_length	int	1	Number of observations per unit of time. Ex: 24 Hourly data.
model	str	Z	Controlling state-space-equations.
alias	str	CES	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

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AutoCES.fit

 AutoCES.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the Complex Exponential Smoothing model.

Fit the Complex Exponential Smoothing model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			Complex Exponential Smoothing fitted model.

---

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AutoCES.predict

 AutoCES.predict (h:int, X:Optional[numpy.ndarray]=None,
                  level:Optional[List[int]]=None)

Predict with fitted Exponential Smoothing.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

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AutoCES.predict_in_sample

 AutoCES.predict_in_sample (level:Optional[List[int]]=None)

Access fitted Exponential Smoothing insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

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AutoCES.forecast

 AutoCES.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                   X_future:Optional[numpy.ndarray]=None,
                   level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient Complex Exponential Smoothing predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenpus of shape (h, n_x).
level	Optional	None
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

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AutoCES.forward

 AutoCES.forward (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                  X_future:Optional[numpy.ndarray]=None,
                  level:Optional[List[int]]=None, fitted:bool=False)

Apply fitted Complex Exponential Smoothing to a new time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenpus of shape (h, n_x).
level	Optional	None
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import AutoCES
from statsforecast.utils import AirPassengers as ap

# CES' usage example
# Multiplicative trend, optimal error and seasonality
ces = AutoCES(model='Z',  
              season_length=4)
ces = ces.fit(y=ap)
y_hat_dict = ces.predict(h=4)
y_hat_dict

AutoTheta

---

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AutoTheta

 AutoTheta (season_length:int=1, decomposition_type:str='multiplicative',
            model:Optional[str]=None, alias:str='AutoTheta', prediction_in
            tervals:Optional[statsforecast.utils.ConformalIntervals]=None)

*AutoTheta model.

Automatically selects the best Theta (Standard Theta Model (‘STM’), Optimized Theta Model (‘OTM’), Dynamic Standard Theta Model (‘DSTM’), Dynamic Optimized Theta Model (‘DOTM’)) model using mse.*

	Type	Default	Details
season_length	int	1	Number of observations per unit of time. Ex: 24 Hourly data.
decomposition_type	str	multiplicative	Sesonal decomposition type, ‘multiplicative’ (default) or ‘additive’.
model	Optional	None	Controlling Theta Model. By default searchs the best model.
alias	str	AutoTheta	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

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AutoTheta.fit

 AutoTheta.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the AutoTheta model.

Fit an AutoTheta model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			AutoTheta fitted model.

---

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AutoTheta.predict

 AutoTheta.predict (h:int, X:Optional[numpy.ndarray]=None,
                    level:Optional[List[int]]=None)

Predict with fitted AutoTheta.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

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AutoTheta.predict_in_sample

 AutoTheta.predict_in_sample (level:Optional[List[int]]=None)

Access fitted AutoTheta insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

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AutoTheta.forecast

 AutoTheta.forecast (y:numpy.ndarray, h:int,
                     X:Optional[numpy.ndarray]=None,
                     X_future:Optional[numpy.ndarray]=None,
                     level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient AutoTheta predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

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AutoTheta.forward

 AutoTheta.forward (y:numpy.ndarray, h:int,
                    X:Optional[numpy.ndarray]=None,
                    X_future:Optional[numpy.ndarray]=None,
                    level:Optional[List[int]]=None, fitted:bool=False)

Apply fitted AutoTheta to a new time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import AutoTheta
from statsforecast.utils import AirPassengers as ap

# AutoTheta's usage example
theta = AutoTheta(season_length=4)
theta = theta.fit(y=ap)
y_hat_dict = theta.predict(h=4)
y_hat_dict

AutoMFLES

---

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AutoMFLES

 AutoMFLES (test_size:int,
            season_length:Union[int,List[int],NoneType]=None,
            n_windows:int=2, config:Optional[Dict[str,Any]]=None,
            step_size:Optional[int]=None, metric:str='smape',
            verbose:bool=False, prediction_intervals:Optional[statsforecas
            t.utils.ConformalIntervals]=None, alias:str='AutoMFLES')

AutoMFLES

	Type	Default	Details
test_size	int		Forecast horizon used during cross validation.
season_length	Union	None	Number of observations per unit of time. Ex: 24 Hourly data.
n_windows	int	2	Number of windows used for cross validation.
config	Optional	None	Mapping from parameter name (from the init arguments of MFLES) to a list of values to try. If None, will use defaults.
step_size	Optional	None	Step size between each cross validation window. If None will be set to test_size.
metric	str	smape	Metric used to select the best model. Possible options are: ‘smape’, ‘mape’, ‘mse’ and ‘mae’.
verbose	bool	False	Print debugging information.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.
alias	str	AutoMFLES	Custom name of the model.

---

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AutoMFLES.fit

 AutoMFLES.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

Fit the model

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Exogenous of shape (t, n_x).
Returns	AutoMFLES		Fitted AutoMFLES object.

---

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AutoMFLES.predict

 AutoMFLES.predict (h:int, X:Optional[numpy.ndarray]=None,
                    level:Optional[List[int]]=None)

Predict with fitted AutoMFLES.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Exogenous of shape (h, n_x).
level	Optional	None
Returns	Dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

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AutoMFLES.predict_in_sample

 AutoMFLES.predict_in_sample (level:Optional[List[int]]=None)

Access fitted AutoMFLES insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	Dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

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AutoMFLES.forecast

 AutoMFLES.forecast (y:numpy.ndarray, h:int,
                     X:Optional[numpy.ndarray]=None,
                     X_future:Optional[numpy.ndarray]=None,
                     level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient AutoMFLES predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
h	int		Forecast horizon.
X	Optional	None	Insample exogenous of shape (t, n_x).
X_future	Optional	None	Exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	Dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

AutoTBATS

---

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AutoTBATS

 AutoTBATS (season_length:Union[int,List[int]],
            use_boxcox:Optional[bool]=None, bc_lower_bound:float=0.0,
            bc_upper_bound:float=1.0, use_trend:Optional[bool]=None,
            use_damped_trend:Optional[bool]=None,
            use_arma_errors:bool=True, alias:str='AutoTBATS')

*AutoTBATS model.

Automatically selects the best TBATS model from all feasible combinations of the parameters use_boxcox, use_trend, use_damped_trend, and use_arma_errors. Selection is made using the AIC. Default value for use_arma_errors is True since this enables the evaluation of models with and without ARMA errors.*

	Type	Default	Details
season_length	Union
use_boxcox	Optional	None	Whether or not to use a Box-Cox transformation. By default tries both.
bc_lower_bound	float	0.0	Lower bound for the Box-Cox transformation.
bc_upper_bound	float	1.0	Upper bound for the Box-Cox transformation.
use_trend	Optional	None	Whether or not to use a trend component. By default tries both.
use_damped_trend	Optional	None	Whether or not to dampen the trend component. By default tries both.
use_arma_errors	bool	True	Whether or not to use a ARMA errors. Default is True and this evaluates both models.
alias	str	AutoTBATS	Custom name of the model.

---

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AutoTBATS.fit

 AutoTBATS.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit TBATS model.

Fit TBATS model to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Ignored
Returns			TBATS model.

---

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AutoTBATS.predict

 AutoTBATS.predict (h:int, X:Optional[numpy.ndarray]=None,
                    level:Optional[List[int]]=None)

Predict with fitted TBATS model.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

AutoTBATS.predict_in_sample

 AutoTBATS.predict_in_sample (level:Optional[Tuple[int]]=None)

Access fitted TBATS model predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

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AutoTBATS.forecast

 AutoTBATS.forecast (y:numpy.ndarray, h:int,
                     X:Optional[numpy.ndarray]=None,
                     X_future:Optional[numpy.ndarray]=None,
                     level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient TBATS model.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None
X_future	Optional	None
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

ARIMA family

ARIMA

---

source

ARIMA

 ARIMA (order:Tuple[int,int,int]=(0, 0, 0), season_length:int=1,
        seasonal_order:Tuple[int,int,int]=(0, 0, 0),
        include_mean:bool=True, include_drift:bool=False,
        include_constant:Optional[bool]=None,
        blambda:Optional[float]=None, biasadj:bool=False, method:str='CSS-
        ML', fixed:Optional[dict]=None, alias:str='ARIMA', prediction_inte
        rvals:Optional[statsforecast.utils.ConformalIntervals]=None)

*ARIMA model.

AutoRegressive Integrated Moving Average model.*

	Type	Default	Details
order	Tuple	(0, 0, 0)	A specification of the non-seasonal part of the ARIMA model: the three components (p, d, q) are the AR order, the degree of differencing, and the MA order.
season_length	int	1	Number of observations per unit of time. Ex: 24 Hourly data.
seasonal_order	Tuple	(0, 0, 0)	A specification of the seasonal part of the ARIMA model. (P, D, Q) for the AR order, the degree of differencing, the MA order.
include_mean	bool	True	Should the ARIMA model include a mean term? The default is True for undifferenced series, False for differenced ones (where a mean would not affect the fit nor predictions).
include_drift	bool	False	Should the ARIMA model include a linear drift term? (i.e., a linear regression with ARIMA errors is fitted.)
include_constant	Optional	None	If True, then includ_mean is set to be True for undifferenced series and include_drift is set to be True for differenced series. Note that if there is more than one difference taken, no constant is included regardless of the value of this argument. This is deliberate as otherwise quadratic and higher order polynomial trends would be induced.
blambda	Optional	None	Box-Cox transformation parameter.
biasadj	bool	False	Use adjusted back-transformed mean Box-Cox.
method	str	CSS-ML	Fitting method: maximum likelihood or minimize conditional sum-of-squares. The default (unless there are missing values) is to use conditional-sum-of-squares to find starting values, then maximum likelihood.
fixed	Optional	None	Dictionary containing fixed coefficients for the arima model. Example: {'ar1': 0.5, 'ma2': 0.75}. For autoregressive terms use the ar{i} keys. For its seasonal version use sar{i}. For moving average terms use the ma{i} keys. For its seasonal version use sma{i}. For intercept and drift use the intercept and drift keys. For exogenous variables use the ex_{i} keys.
alias	str	ARIMA	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

ARIMA.fit

 ARIMA.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

Fit the model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			Fitted model.

---

source

ARIMA.predict

 ARIMA.predict (h:int, X:Optional[numpy.ndarray]=None,
                level:Optional[List[int]]=None)

Predict with fitted model.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

ARIMA.predict_in_sample

 ARIMA.predict_in_sample (level:Optional[List[int]]=None)

Access fitted insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

ARIMA.forecast

 ARIMA.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                 X_future:Optional[numpy.ndarray]=None,
                 level:Optional[List[int]]=None, fitted:bool=False)

*Memory efficient predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x) optional exogenous.
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

ARIMA.forward

 ARIMA.forward (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                X_future:Optional[numpy.ndarray]=None,
                level:Optional[List[int]]=None, fitted:bool=False)

Apply fitted model to a new time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import ARIMA
from statsforecast.utils import AirPassengers as ap

# ARIMA's usage example
arima = ARIMA(order=(1, 0, 0), season_length=12)
arima = arima.fit(y=ap)
y_hat_dict = arima.predict(h=4, level=[80])
y_hat_dict

AutoRegressive

---

source

AutoRegressive

 AutoRegressive (lags:Tuple[int,List], include_mean:bool=True,
                 include_drift:bool=False, blambda:Optional[float]=None,
                 biasadj:bool=False, method:str='CSS-ML',
                 fixed:Optional[dict]=None, alias:str='AutoRegressive', pr
                 ediction_intervals:Optional[statsforecast.utils.Conformal
                 Intervals]=None)

Simple Autoregressive model.

	Type	Default	Details
lags	Tuple		Number of lags to include in the model. If an int is passed then all lags up to lags are considered. If a list, only the elements of the list are considered as lags.
include_mean	bool	True	Should the AutoRegressive model include a mean term? The default is True for undifferenced series, False for differenced ones (where a mean would not affect the fit nor predictions).
include_drift	bool	False	Should the AutoRegressive model include a linear drift term? (i.e., a linear regression with AutoRegressive errors is fitted.)
blambda	Optional	None	Box-Cox transformation parameter.
biasadj	bool	False	Use adjusted back-transformed mean Box-Cox.
method	str	CSS-ML	Fitting method: maximum likelihood or minimize conditional sum-of-squares. The default (unless there are missing values) is to use conditional-sum-of-squares to find starting values, then maximum likelihood.
fixed	Optional	None	Dictionary containing fixed coefficients for the AutoRegressive model. Example: {'ar1': 0.5, 'ar5': 0.75}. For autoregressive terms use the ar{i} keys.
alias	str	AutoRegressive	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

AutoRegressive.fit

 AutoRegressive.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

Fit the model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			Fitted model.

---

source

AutoRegressive.predict

 AutoRegressive.predict (h:int, X:Optional[numpy.ndarray]=None,
                         level:Optional[List[int]]=None)

Predict with fitted model.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

AutoRegressive.predict_in_sample

 AutoRegressive.predict_in_sample (level:Optional[List[int]]=None)

Access fitted insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

AutoRegressive.forecast

 AutoRegressive.forecast (y:numpy.ndarray, h:int,
                          X:Optional[numpy.ndarray]=None,
                          X_future:Optional[numpy.ndarray]=None,
                          level:Optional[List[int]]=None,
                          fitted:bool=False)

*Memory efficient predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x) optional exogenous.
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

AutoRegressive.forward

 AutoRegressive.forward (y:numpy.ndarray, h:int,
                         X:Optional[numpy.ndarray]=None,
                         X_future:Optional[numpy.ndarray]=None,
                         level:Optional[List[int]]=None,
                         fitted:bool=False)

Apply fitted model to a new time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import AutoRegressive
from statsforecast.utils import AirPassengers as ap

# AutoRegressive's usage example
ar = AutoRegressive(lags=[12])
ar = ar.fit(y=ap)
y_hat_dict = ar.predict(h=4, level=[80])
y_hat_dict

ExponentialSmoothing

SimpleSmooth

---

source

SimpleExponentialSmoothing

 SimpleExponentialSmoothing (alpha:float, alias:str='SES', prediction_inte
                             rvals:Optional[statsforecast.utils.ConformalI
                             ntervals]=None)

*SimpleExponentialSmoothing model.

Uses a weighted average of all past observations where the weights decrease exponentially into the past. Suitable for data with no clear trend or seasonality. Assuming there are $t$ observations, the one-step forecast is given by: $\hat{y}_{t+1} = \alpha y_t + (1-\alpha) \hat{y}_{t-1}$

The rate $0 \leq \alpha \leq 1$ at which the weights decrease is called the smoothing parameter. When $\alpha = 1$, SES is equal to the naive method.*

	Type	Default	Details
alpha	float		Smoothing parameter.
alias	str	SES	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

SimpleExponentialSmoothing.forecast

 SimpleExponentialSmoothing.forecast (y:numpy.ndarray, h:int,
                                      X:Optional[numpy.ndarray]=None, X_fu
                                      ture:Optional[numpy.ndarray]=None,
                                      level:Optional[List[int]]=None,
                                      fitted:bool=False)

*Memory Efficient SimpleExponentialSmoothing predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

SimpleExponentialSmoothing.fit

 SimpleExponentialSmoothing.fit (y:numpy.ndarray,
                                 X:Optional[numpy.ndarray]=None)

*Fit the SimpleExponentialSmoothing model.

Fit an SimpleExponentialSmoothing to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			SimpleExponentialSmoothing fitted model.

---

source

SimpleExponentialSmoothing.predict

 SimpleExponentialSmoothing.predict (h:int,
                                     X:Optional[numpy.ndarray]=None,
                                     level:Optional[List[int]]=None)

Predict with fitted SimpleExponentialSmoothing.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

SimpleExponentialSmoothing.predict_in_sample

 SimpleExponentialSmoothing.predict_in_sample ()

Access fitted SimpleExponentialSmoothing insample predictions.

from statsforecast.models import SimpleExponentialSmoothing
from statsforecast.utils import AirPassengers as ap

# SimpleExponentialSmoothing's usage example
ses = SimpleExponentialSmoothing(alpha=0.5)
ses = ses.fit(y=ap)
y_hat_dict = ses.predict(h=4)
y_hat_dict

SimpleSmoothOptimized

---

source

SimpleExponentialSmoothingOptimized

 SimpleExponentialSmoothingOptimized (alias:str='SESOpt', prediction_inter
                                      vals:Optional[statsforecast.utils.Co
                                      nformalIntervals]=None)

*SimpleExponentialSmoothing model.

Uses a weighted average of all past observations where the weights decrease exponentially into the past. Suitable for data with no clear trend or seasonality. Assuming there are $t$ observations, the one-step forecast is given by: $\hat{y}_{t+1} = \alpha y_t + (1-\alpha) \hat{y}_{t-1}$

The smoothing parameter $\alpha^*$ is optimized by square error minimization.*

	Type	Default	Details
alias	str	SESOpt
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.

---

source

SimpleExponentialSmoothingOptimized.fit

 SimpleExponentialSmoothingOptimized.fit (y:numpy.ndarray,
                                          X:Optional[numpy.ndarray]=None)

*Fit the SimpleExponentialSmoothingOptimized model.

Fit an SimpleExponentialSmoothingOptimized to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			SimpleExponentialSmoothingOptimized fitted model.

---

source

SimpleExponentialSmoothingOptimized.predict

 SimpleExponentialSmoothingOptimized.predict (h:int,
                                              X:Optional[numpy.ndarray]=No
                                              ne, level:Optional[List[int]
                                              ]=None)

Predict with fitted SimpleExponentialSmoothingOptimized.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

SimpleExponentialSmoothingOptimized.predict_in_sample

 SimpleExponentialSmoothingOptimized.predict_in_sample ()

Access fitted SimpleExponentialSmoothingOptimized insample predictions.

---

source

SimpleExponentialSmoothingOptimized.forecast

 SimpleExponentialSmoothingOptimized.forecast (y:numpy.ndarray, h:int,
                                               X:Optional[numpy.ndarray]=N
                                               one, X_future:Optional[nump
                                               y.ndarray]=None, level:Opti
                                               onal[List[int]]=None,
                                               fitted:bool=False)

*Memory Efficient SimpleExponentialSmoothingOptimized predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import SimpleExponentialSmoothingOptimized
from statsforecast.utils import AirPassengers as ap

# SimpleExponentialSmoothingOptimized's usage example
seso = SimpleExponentialSmoothingOptimized()
seso = seso.fit(y=ap)
y_hat_dict = seso.predict(h=4)
y_hat_dict

SeasonalSmooth

plt.plot(np.concatenate([ap[6:], seas_es.forecast(ap[6:], h=12)['mean']]))

---

source

SeasonalExponentialSmoothing

 SeasonalExponentialSmoothing (season_length:int, alpha:float,
                               alias:str='SeasonalES', prediction_interval
                               s:Optional[statsforecast.utils.ConformalInt
                               ervals]=None)

*SeasonalExponentialSmoothing model.

Uses a weighted average of all past observations where the weights decrease exponentially into the past. Suitable for data with no clear trend or seasonality. Assuming there are $t$ observations and season $s$, the one-step forecast is given by: $\hat{y}_{t+1,s} = \alpha y_t + (1-\alpha) \hat{y}_{t-1,s}$*

	Type	Default	Details
season_length	int		Number of observations per unit of time. Ex: 24 Hourly data.
alpha	float		Smoothing parameter.
alias	str	SeasonalES	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.

---

source

SeasonalExponentialSmoothing.fit

 SeasonalExponentialSmoothing.fit (y:numpy.ndarray,
                                   X:Optional[numpy.ndarray]=None)

*Fit the SeasonalExponentialSmoothing model.

Fit an SeasonalExponentialSmoothing to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			SeasonalExponentialSmoothing fitted model.

---

source

SeasonalExponentialSmoothing.predict

 SeasonalExponentialSmoothing.predict (h:int,
                                       X:Optional[numpy.ndarray]=None,
                                       level:Optional[List[int]]=None)

Predict with fitted SeasonalExponentialSmoothing.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

SeasonalExponentialSmoothing.predict_in_sample

 SeasonalExponentialSmoothing.predict_in_sample ()

Access fitted SeasonalExponentialSmoothing insample predictions.

---

source

SeasonalExponentialSmoothing.forecast

 SeasonalExponentialSmoothing.forecast (y:numpy.ndarray, h:int,
                                        X:Optional[numpy.ndarray]=None, X_
                                        future:Optional[numpy.ndarray]=Non
                                        e, level:Optional[List[int]]=None,
                                        fitted:bool=False)

*Memory Efficient SeasonalExponentialSmoothing predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import SeasonalExponentialSmoothing
from statsforecast.utils import AirPassengers as ap

# SeasonalExponentialSmoothing's usage example
model = SeasonalExponentialSmoothing(alpha=0.5, season_length=12)
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

SeasonalSmoothOptimized

---

source

SeasonalExponentialSmoothingOptimized

 SeasonalExponentialSmoothingOptimized (season_length:int,
                                        alias:str='SeasESOpt', prediction_
                                        intervals:Optional[statsforecast.u
                                        tils.ConformalIntervals]=None)

*SeasonalExponentialSmoothingOptimized model.

Uses a weighted average of all past observations where the weights decrease exponentially into the past. Suitable for data with no clear trend or seasonality. Assuming there are $t$ observations and season $s$, the one-step forecast is given by: $\hat{y}_{t+1,s} = \alpha y_t + (1-\alpha) \hat{y}_{t-1,s}$

The smoothing parameter $\alpha^*$ is optimized by square error minimization.*

	Type	Default	Details
season_length	int		Number of observations per unit of time. Ex: 24 Hourly data.
alias	str	SeasESOpt	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.

---

source

SeasonalExponentialSmoothingOptimized.forecast

 SeasonalExponentialSmoothingOptimized.forecast (y:numpy.ndarray, h:int,
                                                 X:Optional[numpy.ndarray]
                                                 =None, X_future:Optional[
                                                 numpy.ndarray]=None, leve
                                                 l:Optional[List[int]]=Non
                                                 e, fitted:bool=False)

*Memory Efficient SeasonalExponentialSmoothingOptimized predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

SeasonalExponentialSmoothingOptimized.fit

 SeasonalExponentialSmoothingOptimized.fit (y:numpy.ndarray,
                                            X:Optional[numpy.ndarray]=None
                                            )

*Fit the SeasonalExponentialSmoothingOptimized model.

Fit an SeasonalExponentialSmoothingOptimized to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			SeasonalExponentialSmoothingOptimized fitted model.

---

source

SeasonalExponentialSmoothingOptimized.predict

 SeasonalExponentialSmoothingOptimized.predict (h:int,
                                                X:Optional[numpy.ndarray]=
                                                None, level:Optional[List[
                                                int]]=None)

Predict with fitted SeasonalExponentialSmoothingOptimized.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

SeasonalExponentialSmoothingOptimized.predict_in_sample

 SeasonalExponentialSmoothingOptimized.predict_in_sample ()

Access fitted SeasonalExponentialSmoothingOptimized insample predictions.

from statsforecast.models import SeasonalExponentialSmoothingOptimized
from statsforecast.utils import AirPassengers as ap

# SeasonalExponentialSmoothingOptimized's usage example
model = SeasonalExponentialSmoothingOptimized(season_length=12)
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

Holt’s method

---

source

Holt

 Holt (season_length:int=1, error_type:str='A', alias:str='Holt', predicti
       on_intervals:Optional[statsforecast.utils.ConformalIntervals]=None)

*Holt’s method.

Also known as double exponential smoothing, Holt’s method is an extension of exponential smoothing for series with a trend. This implementation returns the corresponding ETS model with additive (A) or multiplicative (M) errors (so either ‘AAN’ or ‘MAN’).*

	Type	Default	Details
season_length	int	1	Number of observations per unit of time. Ex: 12 Monthly data.
error_type	str	A	The type of error of the ETS model. Can be additive (A) or multiplicative (M).
alias	str	Holt	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

Holt.forecast

 Holt.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                X_future:Optional[numpy.ndarray]=None,
                level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient Exponential Smoothing predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenpus of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

Holt.fit

 Holt.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the Exponential Smoothing model.

Fit an Exponential Smoothing model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			Exponential Smoothing fitted model.

---

source

Holt.predict

 Holt.predict (h:int, X:Optional[numpy.ndarray]=None,
               level:Optional[List[int]]=None)

Predict with fitted Exponential Smoothing.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenpus of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

Holt.predict_in_sample

 Holt.predict_in_sample (level:Optional[List[int]]=None)

Access fitted Exponential Smoothing insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

Holt.forward

 Holt.forward (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
               X_future:Optional[numpy.ndarray]=None,
               level:Optional[List[int]]=None, fitted:bool=False)

Apply fitted Exponential Smoothing model to a new time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenpus of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import Holt
from statsforecast.utils import AirPassengers as ap

# Holt's usage example
model = Holt(season_length=12, error_type='A')
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

Holt-Winters’ method

---

source

HoltWinters

 HoltWinters (season_length:int=1, error_type:str='A',
              alias:str='HoltWinters', prediction_intervals:Optional[stats
              forecast.utils.ConformalIntervals]=None)

*Holt-Winters’ method.

Also known as triple exponential smoothing, Holt-Winters’ method is an extension of exponential smoothing for series that contain both trend and seasonality. This implementation returns the corresponding ETS model with additive (A) or multiplicative (M) errors (so either ‘AAA’ or ‘MAM’).*

	Type	Default	Details
season_length	int	1	season length
error_type	str	A	error type
alias	str	HoltWinters	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

HoltWinters.forecast

 HoltWinters.forecast (y:numpy.ndarray, h:int,
                       X:Optional[numpy.ndarray]=None,
                       X_future:Optional[numpy.ndarray]=None,
                       level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient Exponential Smoothing predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenpus of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

HoltWinters.fit

 HoltWinters.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the Exponential Smoothing model.

Fit an Exponential Smoothing model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			Exponential Smoothing fitted model.

---

source

HoltWinters.predict

 HoltWinters.predict (h:int, X:Optional[numpy.ndarray]=None,
                      level:Optional[List[int]]=None)

Predict with fitted Exponential Smoothing.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenpus of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

HoltWinters.predict_in_sample

 HoltWinters.predict_in_sample (level:Optional[List[int]]=None)

Access fitted Exponential Smoothing insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

HoltWinters.forward

 HoltWinters.forward (y:numpy.ndarray, h:int,
                      X:Optional[numpy.ndarray]=None,
                      X_future:Optional[numpy.ndarray]=None,
                      level:Optional[List[int]]=None, fitted:bool=False)

Apply fitted Exponential Smoothing model to a new time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenpus of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import HoltWinters
from statsforecast.utils import AirPassengers as ap

# Holt-Winters' usage example
model = HoltWinters(season_length=12, error_type='A')
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

Baseline Models

HistoricAverage

---

source

HistoricAverage

 HistoricAverage (alias:str='HistoricAverage', prediction_intervals:Option
                  al[statsforecast.utils.ConformalIntervals]=None)

*HistoricAverage model.

Also known as mean method. Uses a simple average of all past observations. Assuming there are $t$ observations, the one-step forecast is given by: $\hat{y}_{t+1} = \frac{1}{t} \sum_{j=1}^t y_j$*

	Type	Default	Details
alias	str	HistoricAverage
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

HistoricAverage.forecast

 HistoricAverage.forecast (y:numpy.ndarray, h:int,
                           X:Optional[numpy.ndarray]=None,
                           X_future:Optional[numpy.ndarray]=None,
                           level:Optional[List[int]]=None,
                           fitted:bool=False)

*Memory Efficient HistoricAverage predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

HistoricAverage.fit

 HistoricAverage.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the HistoricAverage model.

Fit an HistoricAverage to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns	self		HistoricAverage fitted model.

---

source

HistoricAverage.predict

 HistoricAverage.predict (h:int, X:Optional[numpy.ndarray]=None,
                          level:Optional[List[int]]=None)

Predict with fitted HistoricAverage.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

HistoricAverage.predict_in_sample

 HistoricAverage.predict_in_sample (level:Optional[List[int]]=None)

Access fitted HistoricAverage insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions.

from statsforecast.models import HistoricAverage
from statsforecast.utils import AirPassengers as ap

# HistoricAverage's usage example
model = HistoricAverage()
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

Naive

---

source

Naive

 Naive (alias:str='Naive', prediction_intervals:Optional[statsforecast.uti
        ls.ConformalIntervals]=None)

*Naive model.

All forecasts have the value of the last observation:
$\hat{y}_{t+1} = y_t$ for all $t$*

	Type	Default	Details
alias	str	Naive
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

Naive.forecast

 Naive.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                 X_future:Optional[numpy.ndarray]=None,
                 level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient Naive predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n,).
h	int
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

Naive.fit

 Naive.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the Naive model.

Fit an Naive to a time series (numpy.array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns	self:		Naive fitted model.

---

source

Naive.predict

 Naive.predict (h:int, X:Optional[numpy.ndarray]=None,
                level:Optional[List[int]]=None)

Predict with fitted Naive.

	Type	Default	Details
h	int		forecasting horizon
X	Optional	None	exogenous regressors
level	Optional	None	confidence level
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

Naive.predict_in_sample

 Naive.predict_in_sample (level:Optional[List[int]]=None)

Access fitted Naive insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions.

from statsforecast.models import Naive
from statsforecast.utils import AirPassengers as ap

# Naive's usage example
model = Naive()
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

RandomWalkWithDrift

---

source

RandomWalkWithDrift

 RandomWalkWithDrift (alias:str='RWD', prediction_intervals:Optional[stats
                      forecast.utils.ConformalIntervals]=None)

*RandomWalkWithDrift model.

A variation of the naive method allows the forecasts to change over time. The amout of change, called drift, is the average change seen in the historical data.

$\hat{y}_{t+1} = y_t+\frac{1}{t-1}\sum_{j=1}^t (y_j-y_{j-1}) = y_t+ \frac{y_t-y_1}{t-1}$

From the previous equation, we can see that this is equivalent to extrapolating a line between the first and the last observation.*

	Type	Default	Details
alias	str	RWD	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

RandomWalkWithDrift.forecast

 RandomWalkWithDrift.forecast (y:numpy.ndarray, h:int,
                               X:Optional[numpy.ndarray]=None,
                               X_future:Optional[numpy.ndarray]=None,
                               level:Optional[List[int]]=None,
                               fitted:bool=False)

*Memory Efficient RandomWalkWithDrift predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n,).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	forecasts: dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

RandomWalkWithDrift.fit

 RandomWalkWithDrift.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the RandomWalkWithDrift model.

Fit an RandomWalkWithDrift to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray
X	Optional	None
Returns			RandomWalkWithDrift fitted model.

---

source

RandomWalkWithDrift.predict

 RandomWalkWithDrift.predict (h:int, X:Optional[numpy.ndarray]=None,
                              level:Optional[List[int]]=None)

Predict with fitted RandomWalkWithDrift.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

RandomWalkWithDrift.predict_in_sample

 RandomWalkWithDrift.predict_in_sample (level:Optional[List[int]]=None)

Access fitted RandomWalkWithDrift insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

from statsforecast.models import RandomWalkWithDrift
from statsforecast.utils import AirPassengers as ap

# RandomWalkWithDrift's usage example
model = RandomWalkWithDrift()
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

SeasonalNaive

---

source

SeasonalNaive

 SeasonalNaive (season_length:int, alias:str='SeasonalNaive', prediction_i
                ntervals:Optional[statsforecast.utils.ConformalIntervals]=
                None)

*Seasonal naive model.

A method similar to the naive, but uses the last known observation of the same period (e.g. the same month of the previous year) in order to capture seasonal variations.*

	Type	Default	Details
season_length	int		Number of observations per unit of time. Ex: 24 Hourly data.
alias	str	SeasonalNaive	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

SeasonalNaive.forecast

 SeasonalNaive.forecast (y:numpy.ndarray, h:int,
                         X:Optional[numpy.ndarray]=None,
                         X_future:Optional[numpy.ndarray]=None,
                         level:Optional[List[int]]=None,
                         fitted:bool=False)

*Memory Efficient SeasonalNaive predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

SeasonalNaive.fit

 SeasonalNaive.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the SeasonalNaive model.

Fit an SeasonalNaive to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None
Returns			SeasonalNaive fitted model.

---

source

SeasonalNaive.predict

 SeasonalNaive.predict (h:int, X:Optional[numpy.ndarray]=None,
                        level:Optional[List[int]]=None)

Predict with fitted Naive.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None
level	Optional	None
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

SeasonalNaive.predict_in_sample

 SeasonalNaive.predict_in_sample (level:Optional[List[int]]=None)

Access fitted SeasonalNaive insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

from statsforecast.models import SeasonalNaive
from statsforecast.utils import AirPassengers as ap

# SeasonalNaive's usage example
model = SeasonalNaive(season_length=12)
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

WindowAverage

---

source

WindowAverage

 WindowAverage (window_size:int, alias:str='WindowAverage', prediction_int
                ervals:Optional[statsforecast.utils.ConformalIntervals]=No
                ne)

*WindowAverage model.

Uses the average of the last $k$ observations, with $k$ the length of the window. Wider windows will capture global trends, while narrow windows will reveal local trends. The length of the window selected should take into account the importance of past observations and how fast the series changes.*

	Type	Default	Details
window_size	int		Size of truncated series on which average is estimated.
alias	str	WindowAverage	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.

---

source

WindowAverage.forecast

 WindowAverage.forecast (y:numpy.ndarray, h:int,
                         X:Optional[numpy.ndarray]=None,
                         X_future:Optional[numpy.ndarray]=None,
                         level:Optional[List[int]]=None,
                         fitted:bool=False)

*Memory Efficient WindowAverage predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

WindowAverage.fit

 WindowAverage.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the WindowAverage model.

Fit an WindowAverage to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			WindowAverage fitted model.

---

source

WindowAverage.predict

 WindowAverage.predict (h:int, X:Optional[numpy.ndarray]=None,
                        level:Optional[List[int]]=None)

Predict with fitted WindowAverage.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import WindowAverage
from statsforecast.utils import AirPassengers as ap

# WindowAverage's usage example
model = WindowAverage(window_size=12*4)
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

SeasonalWindowAverage

---

source

SeasonalWindowAverage

 SeasonalWindowAverage (season_length:int, window_size:int,
                        alias:str='SeasWA', prediction_intervals:Optional[
                        statsforecast.utils.ConformalIntervals]=None)

*SeasonalWindowAverage model.

An average of the last $k$ observations of the same period, with $k$ the length of the window.*

	Type	Default	Details
season_length	int
window_size	int		Size of truncated series on which average is estimated.
alias	str	SeasWA	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.

---

source

SeasonalWindowAverage.forecast

 SeasonalWindowAverage.forecast (y:numpy.ndarray, h:int,
                                 X:Optional[numpy.ndarray]=None,
                                 X_future:Optional[numpy.ndarray]=None,
                                 level:Optional[List[int]]=None,
                                 fitted:bool=False)

*Memory Efficient SeasonalWindowAverage predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n,).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

SeasonalWindowAverage.fit

 SeasonalWindowAverage.fit (y:numpy.ndarray,
                            X:Optional[numpy.ndarray]=None)

*Fit the SeasonalWindowAverage model.

Fit an SeasonalWindowAverage to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenpus of shape (t, n_x).
Returns			SeasonalWindowAverage fitted model.

---

source

SeasonalWindowAverage.predict

 SeasonalWindowAverage.predict (h:int, X:Optional[numpy.ndarray]=None,
                                level:Optional[List[int]]=None)

Predict with fitted SeasonalWindowAverage.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import SeasonalWindowAverage
from statsforecast.utils import AirPassengers as ap

# SeasonalWindowAverage's usage example
model = SeasonalWindowAverage(season_length=12, window_size=4)
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

Sparse or Intermittent

ADIDA

---

source

ADIDA

 ADIDA (alias:str='ADIDA', prediction_intervals:Optional[statsforecast.uti
        ls.ConformalIntervals]=None)

*ADIDA model.

Aggregate-Dissagregate Intermittent Demand Approach: Uses temporal aggregation to reduce the number of zero observations. Once the data has been agregated, it uses the optimized SES to generate the forecasts at the new level. It then breaks down the forecast to the original level using equal weights.

ADIDA specializes on sparse or intermittent series are series with very few non-zero observations. They are notoriously hard to forecast, and so, different methods have been developed especifically for them.*

	Type	Default	Details
alias	str	ADIDA	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

ADIDA.forecast

 ADIDA.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                 X_future:Optional[numpy.ndarray]=None,
                 level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient ADIDA predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n,).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

ADIDA.fit

 ADIDA.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the ADIDA model.

Fit an ADIDA to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None
Returns			ADIDA fitted model.

---

source

ADIDA.predict

 ADIDA.predict (h:int, X:Optional[numpy.ndarray]=None,
                level:Optional[List[int]]=None)

Predict with fitted ADIDA.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import ADIDA
from statsforecast.utils import AirPassengers as ap

# ADIDA's usage example
model = ADIDA()
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

CrostonClassic

---

source

CrostonClassic

 CrostonClassic (alias:str='CrostonClassic', prediction_intervals:Optional
                 [statsforecast.utils.ConformalIntervals]=None)

*CrostonClassic model.

A method to forecast time series that exhibit intermittent demand. It decomposes the original time series into a non-zero demand size $z_t$ and inter-demand intervals $p_t$. Then the forecast is given by: $\hat{y}_t = \frac{\hat{z}_t}{\hat{p}_t}$

where $\hat{z}_t$ and $\hat{p}_t$ are forecasted using SES. The smoothing parameter of both components is set equal to 0.1*

	Type	Default	Details
alias	str	CrostonClassic	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

CrostonClassic.forecast

 CrostonClassic.forecast (y:numpy.ndarray, h:int,
                          X:Optional[numpy.ndarray]=None,
                          X_future:Optional[numpy.ndarray]=None,
                          level:Optional[List[int]]=None,
                          fitted:bool=False)

*Memory Efficient CrostonClassic predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

CrostonClassic.fit

 CrostonClassic.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the CrostonClassic model.

Fit an CrostonClassic to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None
Returns			CrostonClassic fitted model.

---

source

CrostonClassic.predict

 CrostonClassic.predict (h:int, X:Optional[numpy.ndarray]=None,
                         level:Optional[List[int]]=None)

Predict with fitted CrostonClassic.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import CrostonClassic
from statsforecast.utils import AirPassengers as ap

# CrostonClassic's usage example
model = CrostonClassic()
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

CrostonOptimized

---

source

CrostonOptimized

 CrostonOptimized (alias:str='CrostonOptimized', prediction_intervals:Opti
                   onal[statsforecast.utils.ConformalIntervals]=None)

*CrostonOptimized model.

A method to forecast time series that exhibit intermittent demand. It decomposes the original time series into a non-zero demand size $z_t$ and inter-demand intervals $p_t$. Then the forecast is given by: $\hat{y}_t = \frac{\hat{z}_t}{\hat{p}_t}$

A variation of the classic Croston’s method where the smooting paramater is optimally selected from the range $[0.1,0.3]$. Both the non-zero demand $z_t$ and the inter-demand intervals $p_t$ are smoothed separately, so their smoothing parameters can be different.*

	Type	Default	Details
alias	str	CrostonOptimized	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.

---

source

CrostonOptimized.forecast

 CrostonOptimized.forecast (y:numpy.ndarray, h:int,
                            X:Optional[numpy.ndarray]=None,
                            X_future:Optional[numpy.ndarray]=None,
                            level:Optional[List[int]]=None,
                            fitted:bool=False)

*Memory Efficient CrostonOptimized predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

CrostonOptimized.fit

 CrostonOptimized.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the CrostonOptimized model.

Fit an CrostonOptimized to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None
Returns			CrostonOptimized fitted model.

---

source

CrostonOptimized.predict

 CrostonOptimized.predict (h:int, X:Optional[numpy.ndarray]=None,
                           level:Optional[List[int]]=None)

Predict with fitted CrostonOptimized.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import CrostonOptimized
from statsforecast.utils import AirPassengers as ap

# CrostonOptimized's usage example
model = CrostonOptimized()
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

CrostonSBA

---

source

CrostonSBA

 CrostonSBA (alias:str='CrostonSBA', prediction_intervals:Optional[statsfo
             recast.utils.ConformalIntervals]=None)

*CrostonSBA model.

A method to forecast time series that exhibit intermittent demand. It decomposes the original time series into a non-zero demand size $z_t$ and inter-demand intervals $p_t$. Then the forecast is given by: $\hat{y}_t = \frac{\hat{z}_t}{\hat{p}_t}$

A variation of the classic Croston’s method that uses a debiasing factor, so that the forecast is given by: $\hat{y}_t = 0.95 \frac{\hat{z}_t}{\hat{p}_t}$*

	Type	Default	Details
alias	str	CrostonSBA	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

CrostonSBA.forecast

 CrostonSBA.forecast (y:numpy.ndarray, h:int,
                      X:Optional[numpy.ndarray]=None,
                      X_future:Optional[numpy.ndarray]=None,
                      level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient CrostonSBA predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

CrostonSBA.fit

 CrostonSBA.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the CrostonSBA model.

Fit an CrostonSBA to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None
Returns			CrostonSBA fitted model.

---

source

CrostonSBA.predict

 CrostonSBA.predict (h:int, X:Optional[numpy.ndarray]=None,
                     level:Optional[List[int]]=None)

Predict with fitted CrostonSBA.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import CrostonSBA
from statsforecast.utils import AirPassengers as ap

# CrostonSBA's usage example
model = CrostonSBA()
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

IMAPA

---

source

IMAPA

 IMAPA (alias:str='IMAPA', prediction_intervals:Optional[statsforecast.uti
        ls.ConformalIntervals]=None)

*IMAPA model.

Intermittent Multiple Aggregation Prediction Algorithm: Similar to ADIDA, but instead of using a single aggregation level, it considers multiple in order to capture different dynamics of the data. Uses the optimized SES to generate the forecasts at the new levels and then combines them using a simple average.*

	Type	Default	Details
alias	str	IMAPA	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

IMAPA.forecast

 IMAPA.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                 X_future:Optional[numpy.ndarray]=None,
                 level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient IMAPA predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

IMAPA.fit

 IMAPA.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the IMAPA model.

Fit an IMAPA to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None
Returns			IMAPA fitted model.

---

source

IMAPA.predict

 IMAPA.predict (h:int, X:Optional[numpy.ndarray]=None,
                level:Optional[List[int]]=None)

Predict with fitted IMAPA.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None
level	Optional	None
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import IMAPA
from statsforecast.utils import AirPassengers as ap

# IMAPA's usage example
model = IMAPA()
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

TSB

---

source

TSB

 TSB (alpha_d:float, alpha_p:float, alias:str='TSB', prediction_intervals:
      Optional[statsforecast.utils.ConformalIntervals]=None)

*TSB model.

Teunter-Syntetos-Babai: A modification of Croston’s method that replaces the inter-demand intervals with the demand probability $d_t$, which is defined as follows.

$$d_t = \begin{cases} 1 & \text{if demand occurs at time t} \\ 0 & \text{otherwise.} \end{cases}$$

Hence, the forecast is given by

$\hat{y}_t= \hat{d}_t\hat{z_t}$

Both $d_t$ and $z_t$ are forecasted using SES. The smooting paramaters of each may differ, like in the optimized Croston’s method.*

	Type	Default	Details
alpha_d	float		Smoothing parameter for demand.
alpha_p	float		Smoothing parameter for probability.
alias	str	TSB	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.

---

source

TSB.forecast

 TSB.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
               X_future:Optional[numpy.ndarray]=None,
               level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient TSB predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

TSB.fit

 TSB.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the TSB model.

Fit an TSB to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None
Returns			TSB fitted model.

---

source

TSB.predict

 TSB.predict (h:int, X:Optional[numpy.ndarray]=None,
              level:Optional[List[int]]=None)

Predict with fitted TSB.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import TSB
from statsforecast.utils import AirPassengers as ap

# TSB's usage example
model = TSB(alpha_d=0.5, alpha_p=0.5)
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

Multiple Seasonalities

MSTL

---

source

MSTL

 MSTL (season_length:Union[int,List[int]], trend_forecaster=AutoETS,
       stl_kwargs:Optional[Dict]=None, alias:str='MSTL', prediction_interv
       als:Optional[statsforecast.utils.ConformalIntervals]=None)

*MSTL model.

The MSTL (Multiple Seasonal-Trend decomposition using LOESS) decomposes the time series in multiple seasonalities using LOESS. Then forecasts the trend using a custom non-seaonal model and each seasonality using a SeasonalNaive model.*

	Type	Default	Details
season_length	Union		Number of observations per unit of time. For multiple seasonalities use a list.
trend_forecaster	AutoETS	AutoETS	StatsForecast model used to forecast the trend component.
stl_kwargs	Optional	None	Extra arguments to pass to statsmodels.tsa.seasonal.STL. The period and seasonal arguments are reserved.
alias	str	MSTL	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

MSTL.fit

 MSTL.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the MSTL model.

Fit MSTL to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None
Returns			MSTL fitted model.

---

source

MSTL.predict

 MSTL.predict (h:int, X:Optional[numpy.ndarray]=None,
               level:Optional[List[int]]=None)

Predict with fitted MSTL.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

MSTL.predict_in_sample

 MSTL.predict_in_sample (level:Optional[List[int]]=None)

Access fitted MSTL insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

MSTL.forecast

 MSTL.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                X_future:Optional[numpy.ndarray]=None,
                level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient MSTL predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

MSTL.forward

 MSTL.forward (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
               X_future:Optional[numpy.ndarray]=None,
               level:Optional[List[int]]=None, fitted:bool=False)

Apply fitted MSTL model to a new time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import MSTL
from statsforecast.utils import AirPassengers as ap

# MSTL's usage example
mstl_model = MSTL(season_length=[3, 12], trend_forecaster=AutoARIMA(prediction_intervals=ConformalIntervals(h=4, n_windows=2)))
mstl_model = mstl_model.fit(y=ap)
y_hat_dict = mstl_model.predict(h=4, level=[80])
y_hat_dict

MFLES

---

source

MFLES

 MFLES (season_length:Union[int,List[int],NoneType]=None,
        fourier_order:Optional[int]=None, max_rounds:int=50,
        ma:Optional[int]=None, alpha:float=1.0, decay:float=-1.0,
        changepoints:bool=True, n_changepoints:Union[float,int]=0.25,
        seasonal_lr:float=0.9, trend_lr:float=0.9, exogenous_lr:float=1.0,
        residuals_lr:float=1.0, cov_threshold:float=0.7,
        moving_medians:bool=False, min_alpha:float=0.05,
        max_alpha:float=1.0, trend_penalty:bool=True,
        multiplicative:Optional[bool]=None, smoother:bool=False,
        robust:Optional[bool]=None, verbose:bool=False, prediction_interva
        ls:Optional[statsforecast.utils.ConformalIntervals]=None,
        alias:str='MFLES')

*MFLES model.

A method to forecast time series based on Gradient Boosted Time Series Decomposition which treats traditional decomposition as the base estimator in the boosting process. Unlike normal gradient boosting, slight learning rates are applied at the component level (trend/seasonality/exogenous).

The method derives its name from some of the underlying estimators that can enter into the boosting procedure, specifically: a simple Median, Fourier functions for seasonality, a simple/piecewise Linear trend, and Exponential Smoothing.*

	Type	Default	Details
season_length	Union	None	Number of observations per unit of time. Ex: 24 Hourly data.
fourier_order	Optional	None	How many fourier sin/cos pairs to create, the larger the number the more complex of a seasonal pattern can be fitted. A lower number leads to smoother results. This is auto-set based on seasonal_period.
max_rounds	int	50	The max number of boosting rounds. The boosting will auto-stop but depending on other parameters such as rs_lr you may want more rounds. Generally more rounds means a smoother fit.
ma	Optional	None	The moving average order to use, this is auto-set based on internal logic. Passing 4 would fit a 4 period moving average on the residual component.
alpha	float	1.0	The alpha which is used in fitting the underlying LASSO when using piecewise functions.
decay	float	-1.0	Effects the slopes of the piecewise-linear basis function.
changepoints	bool	True	Whether to fit for changepoints if all other logic allows for it. If False, MFLES will not ever fit a piecewise trend.
n_changepoints	Union	0.25	Number (if int) or proportion (if float) of changepoint knots to place. The default of 0.25 will place 0.25 * (series length) number of knots.
seasonal_lr	float	0.9	A shrinkage parameter (0 < seasonal_lr <= 1) which penalizes the seasonal fit. A value of 0.9 will flatly multiply the seasonal fit by 0.9 each boosting round, this can be used to allow more signal to the exogenous component.
trend_lr	float	0.9	A shrinkage parameter (0 < trend_lr <= 1) which penalizes the linear trend fit A value of 0.9 will flatly multiply the linear fit by 0.9 each boosting round, this can be used to allow more signal to the seasonality or exogenous components.
exogenous_lr	float	1.0	The shrinkage parameter (0 < exogenous_lr <= 1) which controls how much of the exogenous signal is carried to the next round.
residuals_lr	float	1.0	A shrinkage parameter (0 < residuals_lr <= 1) which penalizes the residual smoothing. A value of 0.9 will flatly multiply the residual fit by 0.9 each boosting round, this can be used to allow more signal to the seasonality or linear components.
cov_threshold	float	0.7	The deseasonalized cov is used to auto-set some logic, lowering the cov_threshold will result in simpler and less complex residual smoothing. If you pass something like 1000 then there will be no safeguards applied.
moving_medians	bool	False	The default behavior is to fit an initial median to the time series. If True, then it will fit a median per seasonal period.
min_alpha	float	0.05	The minimum alpha in the SES ensemble.
max_alpha	float	1.0	The maximum alpha used in the SES ensemble.
trend_penalty	bool	True	Whether to apply a simple penalty to the linear trend component, very useful for dealing with the potentially dangerous piecewise trend.
multiplicative	Optional	None	Auto-set based on internal logic. If True, it will simply take the log of the time series.
smoother	bool	False	If True, then a simple exponential ensemble will be used rather than auto settings.
robust	Optional	None	If True then MFLES will fit using more reserved methods, i.e. not using piecewise trend or moving average residual smoother. Auto-set based on internal logic.
verbose	bool	False	Print debugging information.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.
alias	str	MFLES	Custom name of the model.

---

source

MFLES.fit

 MFLES.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

Fit the model

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Exogenous of shape (t, n_x).
Returns	MFLES		Fitted MFLES object.

---

source

MFLES.predict

 MFLES.predict (h:int, X:Optional[numpy.ndarray]=None,
                level:Optional[List[int]]=None)

Predict with fitted MFLES.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Exogenous of shape (h, n_x).
level	Optional	None
Returns	Dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

MFLES.predict_in_sample

 MFLES.predict_in_sample (level:Optional[List[int]]=None)

Access fitted SklearnModel insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	Dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

MFLES.forecast

 MFLES.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                 X_future:Optional[numpy.ndarray]=None,
                 level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient MFLES predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
h	int		Forecast horizon.
X	Optional	None	Insample exogenous of shape (t, n_x).
X_future	Optional	None	Exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	Dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

TBATS

---

source

TBATS

 TBATS (season_length:Union[int,List[int]],
        use_boxcox:Optional[bool]=True, bc_lower_bound:float=0.0,
        bc_upper_bound:float=1.0, use_trend:Optional[bool]=True,
        use_damped_trend:Optional[bool]=False, use_arma_errors:bool=False,
        alias:str='TBATS')

*Trigonometric Box-Cox transform, ARMA errors, Trend and Seasonal components (TBATS) model.

TBATS is an innovations state space model framework used for forecasting time series with multiple seasonalities. It uses a Box-Cox tranformation, ARMA errors, and a trigonometric representation of the seasonal patterns based on Fourier series.

The name TBATS is an acronym for the key features of the model: Trigonometric, Box-Cox transform, ARMA errors, Trend, and Seasonal components.*

	Type	Default	Details
season_length	Union		Number of observations per unit of time. Ex: 24 Hourly data.
use_boxcox	Optional	True	Whether or not to use a Box-Cox transformation.
bc_lower_bound	float	0.0	Lower bound for the Box-Cox transformation.
bc_upper_bound	float	1.0	Upper bound for the Box-Cox transformation.
use_trend	Optional	True	Whether or not to use a trend component.
use_damped_trend	Optional	False	Whether or not to dampen the trend component.
use_arma_errors	bool	False	Whether or not to use a ARMA errors.
alias	str	TBATS	Custom name of the model.

---

source

TBATS.fit

 TBATS.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit TBATS model.

Fit TBATS model to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Ignored
Returns			TBATS model.

---

source

TBATS.predict

 TBATS.predict (h:int, X:Optional[numpy.ndarray]=None,
                level:Optional[List[int]]=None)

Predict with fitted TBATS model.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

TBATS.predict_in_sample

 TBATS.predict_in_sample (level:Optional[Tuple[int]]=None)

Access fitted TBATS model predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

TBATS.forecast

 TBATS.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                 X_future:Optional[numpy.ndarray]=None,
                 level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient TBATS model.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None
X_future	Optional	None
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

Theta Family

Standard Theta Method

---

source

Theta

 Theta (season_length:int=1, decomposition_type:str='multiplicative',
        alias:str='Theta', prediction_intervals:Optional[statsforecast.uti
        ls.ConformalIntervals]=None)

Standard Theta Method.

	Type	Default	Details
season_length	int	1	Number of observations per unit of time. Ex: 24 Hourly data.
decomposition_type	str	multiplicative	Sesonal decomposition type, ‘multiplicative’ (default) or ‘additive’.
alias	str	Theta	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

Theta.forecast

 Theta.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                 X_future:Optional[numpy.ndarray]=None,
                 level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient AutoTheta predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

Theta.fit

 Theta.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the AutoTheta model.

Fit an AutoTheta model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			AutoTheta fitted model.

---

source

Theta.predict

 Theta.predict (h:int, X:Optional[numpy.ndarray]=None,
                level:Optional[List[int]]=None)

Predict with fitted AutoTheta.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

Theta.predict_in_sample

 Theta.predict_in_sample (level:Optional[List[int]]=None)

Access fitted AutoTheta insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

Theta.forward

 Theta.forward (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                X_future:Optional[numpy.ndarray]=None,
                level:Optional[List[int]]=None, fitted:bool=False)

Apply fitted AutoTheta to a new time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import Theta
from statsforecast.utils import AirPassengers as ap

# Theta's usage example
model = Theta(season_length=12)
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

Optimized Theta Method

---

source

OptimizedTheta

 OptimizedTheta (season_length:int=1,
                 decomposition_type:str='multiplicative',
                 alias:str='OptimizedTheta', prediction_intervals:Optional
                 [statsforecast.utils.ConformalIntervals]=None)

Optimized Theta Method.

	Type	Default	Details
season_length	int	1	Number of observations per unit of time. Ex: 24 Hourly data.
decomposition_type	str	multiplicative	Sesonal decomposition type, ‘multiplicative’ (default) or ‘additive’.
alias	str	OptimizedTheta	Custom name of the model. Default OptimizedTheta.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

OptimizedTheta.forecast

 OptimizedTheta.forecast (y:numpy.ndarray, h:int,
                          X:Optional[numpy.ndarray]=None,
                          X_future:Optional[numpy.ndarray]=None,
                          level:Optional[List[int]]=None,
                          fitted:bool=False)

*Memory Efficient AutoTheta predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

OptimizedTheta.fit

 OptimizedTheta.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the AutoTheta model.

Fit an AutoTheta model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			AutoTheta fitted model.

---

source

OptimizedTheta.predict

 OptimizedTheta.predict (h:int, X:Optional[numpy.ndarray]=None,
                         level:Optional[List[int]]=None)

Predict with fitted AutoTheta.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

OptimizedTheta.predict_in_sample

 OptimizedTheta.predict_in_sample (level:Optional[List[int]]=None)

Access fitted AutoTheta insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

OptimizedTheta.forward

 OptimizedTheta.forward (y:numpy.ndarray, h:int,
                         X:Optional[numpy.ndarray]=None,
                         X_future:Optional[numpy.ndarray]=None,
                         level:Optional[List[int]]=None,
                         fitted:bool=False)

Apply fitted AutoTheta to a new time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import OptimizedTheta
from statsforecast.utils import AirPassengers as ap

# OptimzedThetA's usage example
model = OptimizedTheta(season_length=12)
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

Dynamic Standard Theta Method

---

source

DynamicTheta

 DynamicTheta (season_length:int=1,
               decomposition_type:str='multiplicative',
               alias:str='DynamicTheta', prediction_intervals:Optional[sta
               tsforecast.utils.ConformalIntervals]=None)

Dynamic Standard Theta Method.

	Type	Default	Details
season_length	int	1	Number of observations per unit of time. Ex: 24 Hourly data.
decomposition_type	str	multiplicative	Sesonal decomposition type, ‘multiplicative’ (default) or ‘additive’.
alias	str	DynamicTheta	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

DynamicTheta.forecast

 DynamicTheta.forecast (y:numpy.ndarray, h:int,
                        X:Optional[numpy.ndarray]=None,
                        X_future:Optional[numpy.ndarray]=None,
                        level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient AutoTheta predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

DynamicTheta.fit

 DynamicTheta.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the AutoTheta model.

Fit an AutoTheta model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			AutoTheta fitted model.

---

source

DynamicTheta.predict

 DynamicTheta.predict (h:int, X:Optional[numpy.ndarray]=None,
                       level:Optional[List[int]]=None)

Predict with fitted AutoTheta.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

DynamicTheta.predict_in_sample

 DynamicTheta.predict_in_sample (level:Optional[List[int]]=None)

Access fitted AutoTheta insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

DynamicTheta.forward

 DynamicTheta.forward (y:numpy.ndarray, h:int,
                       X:Optional[numpy.ndarray]=None,
                       X_future:Optional[numpy.ndarray]=None,
                       level:Optional[List[int]]=None, fitted:bool=False)

Apply fitted AutoTheta to a new time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import DynamicTheta
from statsforecast.utils import AirPassengers as ap

# DynStandardThetaMethod's usage example
model = DynamicTheta(season_length=12)
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

Dynamic Optimized Theta Method

---

source

DynamicOptimizedTheta

 DynamicOptimizedTheta (season_length:int=1,
                        decomposition_type:str='multiplicative',
                        alias:str='DynamicOptimizedTheta', prediction_inte
                        rvals:Optional[statsforecast.utils.ConformalInterv
                        als]=None)

Dynamic Optimized Theta Method.

	Type	Default	Details
season_length	int	1	Number of observations per unit of time. Ex: 24 Hourly data.
decomposition_type	str	multiplicative	Sesonal decomposition type, ‘multiplicative’ (default) or ‘additive’.
alias	str	DynamicOptimizedTheta	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

DynamicOptimizedTheta.forecast

 DynamicOptimizedTheta.forecast (y:numpy.ndarray, h:int,
                                 X:Optional[numpy.ndarray]=None,
                                 X_future:Optional[numpy.ndarray]=None,
                                 level:Optional[List[int]]=None,
                                 fitted:bool=False)

*Memory Efficient AutoTheta predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

DynamicOptimizedTheta.fit

 DynamicOptimizedTheta.fit (y:numpy.ndarray,
                            X:Optional[numpy.ndarray]=None)

*Fit the AutoTheta model.

Fit an AutoTheta model to a time series (numpy array) y and optionally exogenous variables (numpy array) X.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns			AutoTheta fitted model.

---

source

DynamicOptimizedTheta.predict

 DynamicOptimizedTheta.predict (h:int, X:Optional[numpy.ndarray]=None,
                                level:Optional[List[int]]=None)

Predict with fitted AutoTheta.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

DynamicOptimizedTheta.predict_in_sample

 DynamicOptimizedTheta.predict_in_sample (level:Optional[List[int]]=None)

Access fitted AutoTheta insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

DynamicOptimizedTheta.forward

 DynamicOptimizedTheta.forward (y:numpy.ndarray, h:int,
                                X:Optional[numpy.ndarray]=None,
                                X_future:Optional[numpy.ndarray]=None,
                                level:Optional[List[int]]=None,
                                fitted:bool=False)

Apply fitted AutoTheta to a new time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

from statsforecast.models import DynamicOptimizedTheta
from statsforecast.utils import AirPassengers as ap

# OptimzedThetaMethod's usage example
model = DynamicOptimizedTheta(season_length=12)
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

ARCH Family

Garch model

---

source

GARCH

 GARCH (p:int=1, q:int=1, alias:str='GARCH', prediction_intervals:Optional
        [statsforecast.utils.ConformalIntervals]=None)

*Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model.

A method for modeling time series that exhibit non-constant volatility over time. The GARCH model assumes that at time $t$, $y_t$ is given by:

$y_t = v_t \sigma_t$

with

$\sigma_t^2 = w + \sum_{i=1}^p a_i y_{t-i}^2 + \sum_{j=1}^q b_j \sigma_{t-j}^2$.

Here $v_t$ is a sequence of iid random variables with zero mean and unit variance. The coefficients $w$, $a_i$, $i=1,...,p$, and $b_j$, $j=1,...,q$ must satisfy the following conditions:

1. $w > 0$ and $a_i, b_j \geq 0$ for all $i$ and $j$.
2. $\sum_{k=1}^{max(p,q)} a_k + b_k < 1$. Here it is assumed that $a_i=0$ for $i>p$ and $b_j=0$ for $j>q$.

The ARCH model is a particular case of the GARCH model when $q=0$.*

	Type	Default	Details
p	int	1	Number of lagged versions of the series.
q	int	1
alias	str	GARCH	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

GARCH.fit

 GARCH.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit GARCH model.

Fit GARCH model to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None
Returns			GARCH model.

---

source

GARCH.predict

 GARCH.predict (h:int, X:Optional[numpy.ndarray]=None,
                level:Optional[List[int]]=None)

Predict with fitted GARCH model.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

GARCH.predict_in_sample

 GARCH.predict_in_sample (level:Optional[List[int]]=None)

Access fitted GARCH model predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

GARCH.forecast

 GARCH.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                 X_future:Optional[numpy.ndarray]=None,
                 level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient GARCH model.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None
X_future	Optional	None
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

ARCH model

---

source

ARCH

 ARCH (p:int=1, alias:str='ARCH', prediction_intervals:Optional[statsforec
       ast.utils.ConformalIntervals]=None)

*Autoregressive Conditional Heteroskedasticity (ARCH) model.

A particular case of the GARCH(p,q) model where $q=0$. It assumes that at time $t$, $y_t$ is given by:

$y_t = \epsilon_t \sigma_t$

with

$\sigma_t^2 = w0 + \sum_{i=1}^p a_i y_{t-i}^2$.

Here $\epsilon_t$ is a sequence of iid random variables with zero mean and unit variance. The coefficients $w$ and $a_i$, $i=1,...,p$ must be nonnegative and $\sum_{k=1}^p a_k < 1$.*

	Type	Default	Details
p	int	1	Number of lagged versions of the series.
alias	str	ARCH	Custom name of the model.
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. By default, the model will compute the native prediction intervals.

---

source

ARCH.fit

 ARCH.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit GARCH model.

Fit GARCH model to a time series (numpy array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None
Returns			GARCH model.

---

source

ARCH.predict

 ARCH.predict (h:int, X:Optional[numpy.ndarray]=None,
               level:Optional[List[int]]=None)

Predict with fitted GARCH model.

	Type	Default	Details
h	int		Forecast horizon.
X	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

ARCH.predict_in_sample

 ARCH.predict_in_sample (level:Optional[List[int]]=None)

Access fitted GARCH model predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

ARCH.forecast

 ARCH.forecast (y:numpy.ndarray, h:int, X:Optional[numpy.ndarray]=None,
                X_future:Optional[numpy.ndarray]=None,
                level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient GARCH model.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None
X_future	Optional	None
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

Machine Learning models

SklearnModel

---

source

SklearnModel

 SklearnModel (model, prediction_intervals:Optional[statsforecast.utils.Co
               nformalIntervals]=None, alias:Optional[str]=None)

scikit-learn model wrapper

	Type	Default	Details
model	sklearn.base.BaseEstimator		scikit-learn estimator
prediction_intervals	Optional	None	Information to compute conformal prediction intervals. This is required for generating future prediction intervals.
alias	Optional	None	Custom name of the model. If None will use the model’s class.

---

source

SklearnModel.fit

 SklearnModel.fit (y:numpy.ndarray, X:numpy.ndarray)

Fit the model.

	Type	Details
y	ndarray	Clean time series of shape (t, ).
X	ndarray	Exogenous of shape (t, n_x).
Returns	SklearnModel	Fitted SklearnModel object.

---

source

SklearnModel.predict

 SklearnModel.predict (h:int, X:numpy.ndarray,
                       level:Optional[List[int]]=None)

Predict with fitted SklearnModel.

	Type	Default	Details
h	int		Forecast horizon.
X	ndarray		Exogenous of shape (h, n_x).
level	Optional	None
Returns	Dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

SklearnModel.predict_in_sample

 SklearnModel.predict_in_sample (level:Optional[List[int]]=None)

Access fitted SklearnModel insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	Dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

SklearnModel.forecast

 SklearnModel.forecast (y:numpy.ndarray, h:int, X:numpy.ndarray,
                        X_future:numpy.ndarray,
                        level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient SklearnModel predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
h	int		Forecast horizon.
X	ndarray		Insample exogenous of shape (t, n_x).
X_future	ndarray		Exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	Dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

Fallback Models

ConstantModel

---

source

ConstantModel

 ConstantModel (constant:float, alias:str='ConstantModel')

*Constant Model.

Returns Constant values.*

---

source

ConstantModel.forecast

 ConstantModel.forecast (y:numpy.ndarray, h:int,
                         X:Optional[numpy.ndarray]=None,
                         X_future:Optional[numpy.ndarray]=None,
                         level:Optional[List[int]]=None,
                         fitted:bool=False)

*Memory Efficient Constant Model predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n,).
h	int
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

ConstantModel.fit

 ConstantModel.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the Constant model.

Fit an Constant Model to a time series (numpy.array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns	self:		Constant fitted model.

---

source

ConstantModel.predict

 ConstantModel.predict (h:int, X:Optional[numpy.ndarray]=None,
                        level:Optional[List[int]]=None)

Predict with fitted ConstantModel.

	Type	Default	Details
h	int		forecasting horizon
X	Optional	None	exogenous regressors
level	Optional	None	confidence level
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

ConstantModel.predict_in_sample

 ConstantModel.predict_in_sample (level:Optional[List[int]]=None)

Access fitted Constant Model insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

ConstantModel.forward

 ConstantModel.forward (y:numpy.ndarray, h:int,
                        X:Optional[numpy.ndarray]=None,
                        X_future:Optional[numpy.ndarray]=None,
                        level:Optional[List[int]]=None, fitted:bool=False)

Apply Constant model predictions to a new/updated time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries constant for point predictions and level_* for probabilistic predictions.

from statsforecast.models import ConstantModel
from statsforecast.utils import AirPassengers as ap

# ConstantModel's usage example
model = ConstantModel(1)
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

ZeroModel

---

source

ZeroModel

 ZeroModel (alias:str='ZeroModel')

*Returns Zero forecasts.

Returns Zero values.*

---

source

ZeroModel.forecast

 ZeroModel.forecast (y:numpy.ndarray, h:int,
                     X:Optional[numpy.ndarray]=None,
                     X_future:Optional[numpy.ndarray]=None,
                     level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient Constant Model predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n,).
h	int
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

ZeroModel.fit

 ZeroModel.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the Constant model.

Fit an Constant Model to a time series (numpy.array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns	self:		Constant fitted model.

---

source

ZeroModel.predict

 ZeroModel.predict (h:int, X:Optional[numpy.ndarray]=None,
                    level:Optional[List[int]]=None)

Predict with fitted ConstantModel.

	Type	Default	Details
h	int		forecasting horizon
X	Optional	None	exogenous regressors
level	Optional	None	confidence level
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

ZeroModel.predict_in_sample

 ZeroModel.predict_in_sample (level:Optional[List[int]]=None)

Access fitted Constant Model insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

---

source

ZeroModel.forward

 ZeroModel.forward (y:numpy.ndarray, h:int,
                    X:Optional[numpy.ndarray]=None,
                    X_future:Optional[numpy.ndarray]=None,
                    level:Optional[List[int]]=None, fitted:bool=False)

Apply Constant model predictions to a new/updated time series.

	Type	Default	Details
y	ndarray		Clean time series of shape (n, ).
h	int		Forecast horizon.
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels for prediction intervals.
fitted	bool	False	Whether or not returns insample predictions.
Returns	dict		Dictionary with entries constant for point predictions and level_* for probabilistic predictions.

from statsforecast.models import ZeroModel
from statsforecast.utils import AirPassengers as ap

# NanModel's usage example
model = ZeroModel()
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

NaNModel

---

source

NaNModel

 NaNModel (alias:str='NaNModel')

*NaN Model.

Returns NaN values.*

---

source

NaNModel.forecast

 NaNModel.forecast (y:numpy.ndarray, h:int,
                    X:Optional[numpy.ndarray]=None,
                    X_future:Optional[numpy.ndarray]=None,
                    level:Optional[List[int]]=None, fitted:bool=False)

*Memory Efficient Constant Model predictions.

This method avoids memory burden due from object storage. It is analogous to fit_predict without storing information. It assumes you know the forecast horizon in advance.*

	Type	Default	Details
y	ndarray		Clean time series of shape (n,).
h	int
X	Optional	None	Optional insample exogenous of shape (t, n_x).
X_future	Optional	None	Optional exogenous of shape (h, n_x).
level	Optional	None	Confidence levels (0-100) for prediction intervals.
fitted	bool	False	Whether or not to return insample predictions.
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

NaNModel.fit

 NaNModel.fit (y:numpy.ndarray, X:Optional[numpy.ndarray]=None)

*Fit the Constant model.

Fit an Constant Model to a time series (numpy.array) y.*

	Type	Default	Details
y	ndarray		Clean time series of shape (t, ).
X	Optional	None	Optional exogenous of shape (t, n_x).
Returns	self:		Constant fitted model.

---

source

NaNModel.predict

 NaNModel.predict (h:int, X:Optional[numpy.ndarray]=None,
                   level:Optional[List[int]]=None)

Predict with fitted ConstantModel.

	Type	Default	Details
h	int		forecasting horizon
X	Optional	None	exogenous regressors
level	Optional	None	confidence level
Returns	dict		Dictionary with entries mean for point predictions and level_* for probabilistic predictions.

---

source

NaNModel.predict_in_sample

 NaNModel.predict_in_sample (level:Optional[List[int]]=None)

Access fitted Constant Model insample predictions.

	Type	Default	Details
level	Optional	None	Confidence levels (0-100) for prediction intervals.
Returns	dict		Dictionary with entries fitted for point predictions and level_* for probabilistic predictions.

from statsforecast.models import NaNModel
from statsforecast.utils import AirPassengers as ap

# NanModel's usage example
model = NaNModel()
model = model.fit(y=ap)
y_hat_dict = model.predict(h=4)
y_hat_dict

References

General

• Hyndman, R.J., & Athanasopoulos, G. (2021). “Forecasting: principles and practice, 3rd edition”. OTexts: Melbourne, Australia. OTexts.com/fpp3 Accessed on July 2022.

• Shmueli, G., & Lichtendahl Jr, K. C. (2016). “Practical time series forecasting with R: A hands-on guide”. Axelrod Schnall Publishers.

Automatic Forecasting

• Rob J. Hyndman, Yeasmin Khandakar (2008). “Automatic Time Series Forecasting: The forecast package for R”.

Exponential Smoothing

• Charles. C. Holt (1957). “Forecasting seasonals and trends by exponentially weighted moving averages”, ONR Research Memorandum, Carnegie Institute of Technology 52.

• Peter R. Winters (1960). “Forecasting sales by exponentially weighted moving averages”. Management Science.

• Hyndman, Rob, et al (2008). “Forecasting with exponential smoothing: the state space approach”.

• Rob J. Hyndman and George Athanasopoulos (2018). “Forecasting principles and practice, Methods with trend”.

• Rob J. Hyndman and George Athanasopoulos (2018). “Forecasting principles and practice, Methods with seasonality”.

Simple Methods

• Rob J. Hyndman and George Athanasopoulos (2018). “Forecasting principles and practice, Simple Methods”.

Sparse Intermittent

• Croston, J. D. (1972). “Forecasting and stock control for intermittent demands”. Journal of the Operational Research Society, 23(3), 289-303.

• Nikolopoulos, K., Syntetos, A. A., Boylan, J. E., Petropoulos, F., & Assimakopoulos, V. (2011). “An aggregate–disaggregate intermittent demand approach (ADIDA) to forecasting: an empirical proposition and analysis”. Journal of the Operational Research Society, 62(3), 544-554.

• Syntetos, A. A., & Boylan, J. E. (2005). “The accuracy of intermittent demand estimates”. International Journal of forecasting, 21(2), 303-314.

• Syntetos, A. A., & Boylan, J. E. (2021). “Intermittent demand forecasting: Context, methods and applications”. John Wiley & Sons.

• Teunter, R. H., Syntetos, A. A., & Babai, M. Z. (2011). “Intermittent demand: Linking forecasting to inventory obsolescence”. European Journal of Operational Research, 214(3), 606-615.

Multiple Seasonalities

• Bandara, Kasun & Hyndman, Rob & Bergmeir, Christoph. (2021). “MSTL: A Seasonal-Trend Decomposition Algorithm for Time Series with Multiple Seasonal Patterns”.

Theta Family

• Jose A. Fiorucci, Tiago R. Pellegrini, Francisco Louzada, Fotios Petropoulos, Anne B. Koehler (2016). “Models for optimising the theta method and their relationship to state space models”. International Journal of Forecasting.

GARCH Model

• Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the econometric society, 987-1007.

• Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of econometrics, 31(3), 307-327.

• Hamilton, J. D. (1994). Time series analysis. Princeton university press.

TBATS Model

• De Livera, A. M., Hyndman, R. J., & Snyder, R. D. (2011). Forecasting time series with complex seasonal patterns using exponential smoothing. Journal of the American statistical association, 106(496), 1513-1527.

• De Livera, Alysha M (2017). Modeling time series with complex seasonal patterns using exponential smoothing. Monash University. Thesis.