> ## 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.
# NHITS
Long-horizon forecasting is challenging because of the *volatility* of
the predictions and the *computational complexity*. To solve this
problem we created the Neural Hierarchical Interpolation for Time Series
(NHITS).
[`NHITS`](https://nixtlaverse.nixtla.io/neuralforecast/models.nhits.html#nhits)
builds upon
[`NBEATS`](https://nixtlaverse.nixtla.io/neuralforecast/models.nbeats.html#nbeats)
and specializes its partial outputs in the different frequencies of the
time series through hierarchical interpolation and multi-rate input
processing. On the long-horizon forecasting task
[`NHITS`](https://nixtlaverse.nixtla.io/neuralforecast/models.nhits.html#nhits)
improved accuracy by 25% on AAAI’s best paper award the
[`Informer`](https://nixtlaverse.nixtla.io/neuralforecast/models.informer.html#informer),
while being 50x faster.
The model is composed of several MLPs with ReLU non-linearities. Blocks
are connected via doubly residual stacking principle with the backcast
$\mathbf{\tilde{y}}_{t-L:t,l}$ and forecast
$\mathbf{\hat{y}}_{t+1:t+H,l}$ outputs of the l-th block. Multi-rate
input pooling, hierarchical interpolation and backcast residual
connections together induce the specialization of the additive
predictions in different signal bands, reducing memory footprint and
computational time, thus improving the architecture parsimony and
accuracy.
**References** -[Boris N. Oreshkin, Dmitri Carpov, Nicolas Chapados,
Yoshua Bengio (2019). “N-BEATS: Neural basis expansion analysis for
interpretable time series
forecasting”.](https://arxiv.org/abs/1905.10437) -[Cristian Challu,
Kin G. Olivares, Boris N. Oreshkin, Federico Garza, Max
Mergenthaler-Canseco, Artur Dubrawski (2023). “NHITS: Neural
Hierarchical Interpolation for Time Series Forecasting”. Accepted at the
Thirty-Seventh AAAI Conference on Artificial
Intelligence.](https://arxiv.org/abs/2201.12886) -[Zhou, H.; Zhang,
S.; Peng, J.; Zhang, S.; Li, J.; Xiong, H.; and Zhang, W. (2020).
“Informer: Beyond Efficient Transformer for Long Sequence Time-Series
Forecasting”. Association for the Advancement of Artificial Intelligence
Conference 2021 (AAAI 2021).](https://arxiv.org/abs/2012.07436)
Figure 1. Neural Hierarchical
Interpolation for Time Series (NHITS).
***
source
### NHITS
> ```text theme={null}
> NHITS (h, input_size, futr_exog_list=None, hist_exog_list=None,
> stat_exog_list=None, exclude_insample_y=False,
> stack_types:list=['identity', 'identity', 'identity'],
> n_blocks:list=[1, 1, 1], mlp_units:list=[[512, 512], [512, 512],
> [512, 512]], n_pool_kernel_size:list=[2, 2, 1],
> n_freq_downsample:list=[4, 2, 1], pooling_mode:str='MaxPool1d',
> interpolation_mode:str='linear', dropout_prob_theta=0.0,
> activation='ReLU', loss=MAE(), valid_loss=None,
> 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)
> ```
\*NHITS
The Neural Hierarchical Interpolation for Time Series (NHITS), is an
MLP-based deep neural architecture with backward and forward residual
links. NHITS tackles volatility and memory complexity challenges, by
locally specializing its sequential predictions into the signals
frequencies with hierarchical interpolation and pooling.
**Parameters:** `h`: int, Forecast horizon. `input_size`: int,
autorregresive inputs size, y=\[1,2,3,4] input\_size=2 ->
y\_\[t-2:t]=\[1,2]. `futr_exog_list`: str list, future exogenous
columns. `hist_exog_list`: str list, historic exogenous columns.
`stat_exog_list`: str list, static exogenous columns.
`exclude_insample_y`: bool=False, the model skips the autoregressive
features y\[t-input\_size:t] if True. `stack_types`: List\[str],
stacks list in the form N \* \[‘identity’], to be deprecated in favor
of `n_stacks`. Note that
len(stack\_types)=len(n\_freq\_downsample)=len(n\_pool\_kernel\_size).
`n_blocks`: List\[int], Number of blocks for each stack. Note that
len(n\_blocks) = len(stack\_types). `mlp_units`: List\[List\[int]],
Structure of hidden layers for each stack type. Each internal list
should contain the number of units of each hidden layer. Note that
len(n\_hidden) = len(stack\_types). `n_pool_kernel_size`: List\[int],
list with the size of the windows to take a max/avg over. Note that
len(stack\_types)=len(n\_freq\_downsample)=len(n\_pool\_kernel\_size).
`n_freq_downsample`: List\[int], list with the stack’s coefficients
(inverse expressivity ratios). Note that
len(stack\_types)=len(n\_freq\_downsample)=len(n\_pool\_kernel\_size).
`pooling_mode`: str, input pooling module from \[‘MaxPool1d’,
‘AvgPool1d’]. `interpolation_mode`: str=‘linear’, interpolation
basis from \[‘linear’, ‘nearest’, ‘cubic’]. `dropout_prob_theta`:
float, Float between (0, 1). Dropout for NHITS basis. `activation`:
str, activation from \[‘ReLU’, ‘Softplus’, ‘Tanh’, ‘SELU’, ‘LeakyReLU’,
‘PReLU’, ‘Sigmoid’]. `loss`: PyTorch module, instantiated train
loss class from [losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).
`valid_loss`: PyTorch module=`loss`, instantiated valid loss class from
[losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).
`max_steps`: int=1000, maximum number of training steps.
`learning_rate`: float=1e-3, Learning rate between (0, 1).
`num_lr_decays`: int=-1, Number of learning rate decays, evenly
distributed across max\_steps. `early_stop_patience_steps`: int=-1,
Number of validation iterations before early stopping.
`val_check_steps`: int=100, Number of training steps between every
validation loss check. `batch_size`: int=32, number of different
series in each batch. `valid_batch_size`: int=None, number of
different series in each validation and test batch, if None uses
batch\_size. `windows_batch_size`: int=1024, number of windows to
sample in each training batch, default uses all.
`inference_windows_batch_size`: int=-1, number of windows to sample in
each inference batch, -1 uses all. `start_padding_enabled`:
bool=False, if True, the model will pad the time series with zeros at
the beginning, by input size. `step_size`: int=1, step size between
each window of temporal data. `scaler_type`: str=‘identity’, type of
scaler for temporal inputs normalization see [temporal
scalers](https://nixtla.github.io/neuralforecast/common.scalers.html).
`random_seed`: int, random\_seed for pytorch initializer and numpy
generators. `drop_last_loader`: bool=False, if True
`TimeSeriesDataLoader` drops last non-full batch. `alias`: str,
optional, Custom name of the model. `optimizer`: Subclass of
‘torch.optim.Optimizer’, optional, user specified optimizer instead of
the default choice (Adam). `optimizer_kwargs`: dict, optional, list
of parameters used by the user specified `optimizer`.
`lr_scheduler`: Subclass of ‘torch.optim.lr\_scheduler.LRScheduler’,
optional, user specified lr\_scheduler instead of the default choice
(StepLR). `lr_scheduler_kwargs`: dict, optional, list of parameters
used by the user specified `lr_scheduler`. \
`dataloader_kwargs`: dict, optional, list of parameters passed into the
PyTorch Lightning dataloader by the `TimeSeriesDataLoader`.
`**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).
**References:** -[Cristian Challu, Kin G. Olivares, Boris N.
Oreshkin, Federico Garza, Max Mergenthaler-Canseco, Artur Dubrawski
(2023). “NHITS: Neural Hierarchical Interpolation for Time Series
Forecasting”. Accepted at the Thirty-Seventh AAAI Conference on
Artificial Intelligence.](https://arxiv.org/abs/2201.12886)\*
***
### NHITS.fit
> ```text theme={null}
> NHITS.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:** `dataset`: NeuralForecast’s
[`TimeSeriesDataset`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).
`val_size`: int, validation size for temporal cross-validation.
`random_seed`: int=None, random\_seed for pytorch initializer and numpy
generators, overwrites model.\_\_init\_\_’s. `test_size`: int, test
size for temporal cross-validation. \*
***
### NHITS.predict
> ```text theme={null}
> NHITS.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:** `dataset`: NeuralForecast’s
[`TimeSeriesDataset`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).
`test_size`: int=None, test size for temporal cross-validation.
`step_size`: int=1, Step size between each window. `random_seed`:
int=None, random\_seed for pytorch initializer and numpy generators,
overwrites model.\_\_init\_\_’s. `quantiles`: list of floats,
optional (default=None), target quantiles to predict.
`**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 NHITS
from neuralforecast.losses.pytorch import DistributionLoss
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
Y_train_df = AirPassengersPanel[AirPassengersPanel.ds=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test
model = NHITS(h=12,
input_size=24,
loss=DistributionLoss(distribution='StudentT', level=[80, 90], return_params=True),
stat_exog_list=['airline1'],
futr_exog_list=['trend'],
n_freq_downsample=[2, 1, 1],
scaler_type='robust',
max_steps=200,
early_stop_patience_steps=2,
inference_windows_batch_size=1,
val_check_steps=10,
learning_rate=1e-3)
fcst = NeuralForecast(models=[model], freq='ME')
fcst.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)
forecasts = fcst.predict(futr_df=Y_test_df)
# Plot quantile predictions
Y_hat_df = forecasts.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['NHITS-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:],
y1=plot_df['NHITS-lo-90'][-12:].values,
y2=plot_df['NHITS-hi-90'][-12:].values,
alpha=0.4, label='level 90')
plt.legend()
plt.grid()
plt.plot()
```
