> ## Documentation Index
> Fetch the complete documentation index at: https://nixtla-old-docs.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# DeepAR

The DeepAR model produces probabilistic forecasts based on an
autoregressive recurrent neural network optimized on panel data using
cross-learning. DeepAR obtains its forecast distribution uses a Markov
Chain Monte Carlo sampler with the following conditional probability:
$\mathbb{P}(\mathbf{y}_{[t+1:t+H]}|\;\mathbf{y}_{[:t]},\; \mathbf{x}^{(f)}_{[:t+H]},\; \mathbf{x}^{(s)})$

where $\mathbf{x}^{(s)}$ are static exogenous inputs,
$\mathbf{x}^{(f)}_{[:t+H]}$ are future exogenous available at the time
of the prediction. The predictions are obtained by transforming the
hidden states $\mathbf{h}_{t}$ into predictive distribution parameters
$\theta_{t}$, and then generating samples $\mathbf{\hat{y}}_{[t+1:t+H]}$
through Monte Carlo sampling trajectories.

$$

\begin{align}
\mathbf{h}_{t} &= \textrm{RNN}([\mathbf{y}_{t},\mathbf{x}^{(f)}_{t+1},\mathbf{x}^{(s)}], \mathbf{h}_{t-1})\\
\mathbf{\theta}_{t}&=\textrm{Linear}(\mathbf{h}_{t}) \\
\hat{y}_{t+1}&=\textrm{sample}(\;\mathrm{P}(y_{t+1}\;|\;\mathbf{\theta}_{t})\;)
\end{align}

$$

**References**<br /> - [David Salinas, Valentin Flunkert, Jan Gasthaus,
Tim Januschowski (2020). “DeepAR: Probabilistic forecasting with
autoregressive recurrent networks”. International Journal of
Forecasting.](https://www.sciencedirect.com/science/article/pii/S0169207019301888)<br /> -
[Alexander Alexandrov et. al (2020). “GluonTS: Probabilistic and Neural
Time Series Modeling in Python”. Journal of Machine Learning
Research.](https://www.jmlr.org/papers/v21/19-820.html)<br />

> **Exogenous Variables, Losses, and Parameters Availability**
>
> Given the sampling procedure during inference, DeepAR only supports
> [`DistributionLoss`](https://nixtlaverse.nixtla.io/neuralforecast/losses.pytorch.html#distributionloss)
> as training loss.
>
> Note that DeepAR generates a non-parametric forecast distribution
> using Monte Carlo. We use this sampling procedure also during
> validation to make it closer to the inference procedure. Therefore,
> only the
> [`MQLoss`](https://nixtlaverse.nixtla.io/neuralforecast/losses.pytorch.html#mqloss)
> is available for validation.
>
> Aditionally, Monte Carlo implies that historic exogenous variables are
> not available for the model.

<figure>
  <img src="https://mintcdn.com/nixtla-old-docs/x1r-gXtjoZEzq4L2/neuralforecast/imgs_models/deepar.jpeg?fit=max&auto=format&n=x1r-gXtjoZEzq4L2&q=85&s=0ce4cab9af8460e23f2dcbe322fbc81e" alt="Figure 1. DeepAR model, during training the optimization signal comes from likelihood of observations, during inference a recurrent multi-step strategy is used to generate predictive distributions." width="1600" height="909" data-path="neuralforecast/imgs_models/deepar.jpeg" />

  <figcaption aria-hidden="true">Figure 1. DeepAR model, during training
  the optimization signal comes from likelihood of observations, during
  inference a recurrent multi-step strategy is used to generate predictive
  distributions.</figcaption>
</figure>

***

<a href="https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/models/fedformer.py#L214" target="_blank" style={{ float: "right", fontSize: "smaller" }}>source</a>

### Decoder

> ```text theme={null}
>  Decoder (in_features, out_features, hidden_size, hidden_layers)
> ```

\*Multi-Layer Perceptron Decoder

**Parameters:**<br /> `in_features`: int, dimension of input.<br />
`out_features`: int, dimension of output.<br /> `hidden_size`: int,
dimension of hidden layers.<br /> `num_layers`: int, number of hidden
layers.<br />\*

***

<a href="https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/models/deepar.py#L54" target="_blank" style={{ float: "right", fontSize: "smaller" }}>source</a>

### DeepAR

> ```text theme={null}
>  DeepAR (h, input_size:int=-1, h_train:int=1, lstm_n_layers:int=2,
>          lstm_hidden_size:int=128, lstm_dropout:float=0.1,
>          decoder_hidden_layers:int=0, decoder_hidden_size:int=0,
>          trajectory_samples:int=100, stat_exog_list=None,
>          hist_exog_list=None, futr_exog_list=None,
>          exclude_insample_y=False, loss=DistributionLoss(),
>          valid_loss=MAE(), max_steps:int=1000, learning_rate:float=0.001,
>          num_lr_decays:int=3, early_stop_patience_steps:int=-1,
>          val_check_steps:int=100, batch_size:int=32,
>          valid_batch_size:Optional[int]=None, windows_batch_size:int=1024,
>          inference_windows_batch_size:int=-1, start_padding_enabled=False,
>          step_size:int=1, scaler_type:str='identity', random_seed:int=1,
>          drop_last_loader=False, alias:Optional[str]=None, optimizer=None,
>          optimizer_kwargs=None, lr_scheduler=None,
>          lr_scheduler_kwargs=None, dataloader_kwargs=None,
>          **trainer_kwargs)
> ```

\*DeepAR

**Parameters:**<br /> `h`: int, Forecast horizon. <br /> `input_size`: int,
maximum sequence length for truncated train backpropagation. Default -1
uses 3 \* horizon <br /> `h_train`: int, maximum sequence length for
truncated train backpropagation. Default 1.<br /> `lstm_n_layers`: int=2,
number of LSTM layers.<br /> `lstm_hidden_size`: int=128, LSTM hidden
size.<br /> `lstm_dropout`: float=0.1, LSTM dropout.<br />
`decoder_hidden_layers`: int=0, number of decoder MLP hidden layers.
Default: 0 for linear layer. <br /> `decoder_hidden_size`: int=0, decoder
MLP hidden size. Default: 0 for linear layer.<br /> `trajectory_samples`:
int=100, number of Monte Carlo trajectories during inference.<br />
`stat_exog_list`: str list, static exogenous columns.<br />
`hist_exog_list`: str list, historic exogenous columns.<br />
`futr_exog_list`: str list, future exogenous columns.<br />
`exclude_insample_y`: bool=False, the model skips the autoregressive
features y\[t-input\_size:t] if True.<br /> `loss`: PyTorch module,
instantiated train loss class from [losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).<br />
`valid_loss`: PyTorch module=`loss`, instantiated valid loss class from
[losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).<br />
`max_steps`: int=1000, maximum number of training steps.<br />
`learning_rate`: float=1e-3, Learning rate between (0, 1).<br />
`num_lr_decays`: int=-1, Number of learning rate decays, evenly
distributed across max\_steps.<br /> `early_stop_patience_steps`: int=-1,
Number of validation iterations before early stopping.<br />
`val_check_steps`: int=100, Number of training steps between every
validation loss check.<br /> `batch_size`: int=32, number of different
series in each batch.<br /> `valid_batch_size`: int=None, number of
different series in each validation and test batch, if None uses
batch\_size.<br /> `windows_batch_size`: int=1024, number of windows to
sample in each training batch, default uses all.<br />
`inference_windows_batch_size`: int=-1, number of windows to sample in
each inference batch, -1 uses all.<br /> `start_padding_enabled`:
bool=False, if True, the model will pad the time series with zeros at
the beginning, by input size.<br /> `step_size`: int=1, step size between
each window of temporal data.<br /> `scaler_type`: str=‘identity’, type of
scaler for temporal inputs normalization see [temporal
scalers](https://nixtla.github.io/neuralforecast/common.scalers.html).<br />
`random_seed`: int, random\_seed for pytorch initializer and numpy
generators.<br /> `drop_last_loader`: bool=False, if True
`TimeSeriesDataLoader` drops last non-full batch.<br /> `alias`: str,
optional, Custom name of the model.<br /> `optimizer`: Subclass of
‘torch.optim.Optimizer’, optional, user specified optimizer instead of
the default choice (Adam).<br /> `optimizer_kwargs`: dict, optional, list
of parameters used by the user specified `optimizer`.<br />
`lr_scheduler`: Subclass of ‘torch.optim.lr\_scheduler.LRScheduler’,
optional, user specified lr\_scheduler instead of the default choice
(StepLR).<br /> `lr_scheduler_kwargs`: dict, optional, list of parameters
used by the user specified `lr_scheduler`.<br /> `dataloader_kwargs`:
dict, optional, list of parameters passed into the PyTorch Lightning
dataloader by the `TimeSeriesDataLoader`. <br /> `**trainer_kwargs`: int,
keyword trainer arguments inherited from [PyTorch Lighning’s
trainer](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).<br />

**References**<br /> - [David Salinas, Valentin Flunkert, Jan Gasthaus,
Tim Januschowski (2020). “DeepAR: Probabilistic forecasting with
autoregressive recurrent networks”. International Journal of
Forecasting.](https://www.sciencedirect.com/science/article/pii/S0169207019301888)<br /> -
[Alexander Alexandrov et. al (2020). “GluonTS: Probabilistic and Neural
Time Series Modeling in Python”. Journal of Machine Learning
Research.](https://www.jmlr.org/papers/v21/19-820.html)<br />\*

***

### DeepAR.fit

> ```text theme={null}
>  DeepAR.fit (dataset, val_size=0, test_size=0, random_seed=None,
>              distributed_config=None)
> ```

\*Fit.

The `fit` method, optimizes the neural network’s weights using the
initialization parameters (`learning_rate`, `windows_batch_size`, …) and
the `loss` function as defined during the initialization. Within `fit`
we use a PyTorch Lightning `Trainer` that inherits the initialization’s
`self.trainer_kwargs`, to customize its inputs, see [PL’s trainer
arguments](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).

The method is designed to be compatible with SKLearn-like classes and in
particular to be compatible with the StatsForecast library.

By default the `model` is not saving training checkpoints to protect
disk memory, to get them change `enable_checkpointing=True` in
`__init__`.

**Parameters:**<br /> `dataset`: NeuralForecast’s
[`TimeSeriesDataset`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).<br />
`val_size`: int, validation size for temporal cross-validation.<br />
`random_seed`: int=None, random\_seed for pytorch initializer and numpy
generators, overwrites model.\_\_init\_\_’s.<br /> `test_size`: int, test
size for temporal cross-validation.<br />\*

***

### DeepAR.predict

> ```text theme={null}
>  DeepAR.predict (dataset, test_size=None, step_size=1, random_seed=None,
>                  quantiles=None, **data_module_kwargs)
> ```

\*Predict.

Neural network prediction with PL’s `Trainer` execution of
`predict_step`.

**Parameters:**<br /> `dataset`: NeuralForecast’s
[`TimeSeriesDataset`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).<br />
`test_size`: int=None, test size for temporal cross-validation.<br />
`step_size`: int=1, Step size between each window.<br /> `random_seed`:
int=None, random\_seed for pytorch initializer and numpy generators,
overwrites model.\_\_init\_\_’s.<br /> `quantiles`: list of floats,
optional (default=None), target quantiles to predict. <br />
`**data_module_kwargs`: PL’s TimeSeriesDataModule args, see
[documentation](https://pytorch-lightning.readthedocs.io/en/1.6.1/extensions/datamodules.html#using-a-datamodule).\*

## Usage Example

```python theme={null}
import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import DeepAR
from neuralforecast.losses.pytorch import DistributionLoss, MQLoss
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
Y_train_df = AirPassengersPanel[AirPassengersPanel.ds<AirPassengersPanel['ds'].values[-12]] # 132 train
Y_test_df = AirPassengersPanel[AirPassengersPanel.ds>=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test

nf = NeuralForecast(
    models=[DeepAR(h=12,
                   input_size=24,
                   lstm_n_layers=1,
                   trajectory_samples=100,
                   loss=DistributionLoss(distribution='StudentT', level=[80, 90], return_params=True),
                   valid_loss=MQLoss(level=[80, 90]),
                   learning_rate=0.005,
                   stat_exog_list=['airline1'],
                   futr_exog_list=['trend'],
                   max_steps=100,
                   val_check_steps=10,
                   early_stop_patience_steps=-1,
                   scaler_type='standard',
                   enable_progress_bar=True,
                   ),
    ],
    freq='ME'
)
nf.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)
Y_hat_df = nf.predict(futr_df=Y_test_df)

# Plot quantile predictions
Y_hat_df = Y_hat_df.reset_index(drop=False).drop(columns=['unique_id','ds'])
plot_df = pd.concat([Y_test_df, Y_hat_df], axis=1)
plot_df = pd.concat([Y_train_df, plot_df])

plot_df = plot_df[plot_df.unique_id=='Airline1'].drop('unique_id', axis=1)
plt.plot(plot_df['ds'], plot_df['y'], c='black', label='True')
plt.plot(plot_df['ds'], plot_df['DeepAR-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:], 
                 y1=plot_df['DeepAR-lo-90'][-12:].values, 
                 y2=plot_df['DeepAR-hi-90'][-12:].values,
                 alpha=0.4, label='level 90')
plt.legend()
plt.grid()
plt.plot()
```