> ## 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.

# DLinear

DLinear is a simple and fast yet accurate time series forecasting model
for long-horizon forecasting.

The architecture has the following distinctive features: - Uses
Autoformmer’s trend and seasonality decomposition. - Simple linear
layers for trend and seasonality component.

**References**<br /> - [Zeng, Ailing, et al. “Are transformers effective
for time series forecasting?.” Proceedings of the AAAI conference on
artificial intelligence. Vol. 37. No. 9.
2023.”](https://ojs.aaai.org/index.php/AAAI/article/view/26317)<br />

<figure>
  <img src="https://mintcdn.com/nixtla-old-docs/x1r-gXtjoZEzq4L2/neuralforecast/imgs_models/dlinear.png?fit=max&auto=format&n=x1r-gXtjoZEzq4L2&q=85&s=1d0eba600a3a47ccb84c2a16be7fb3c7" alt="Figure 1. DLinear Architecture." width="1090" height="622" data-path="neuralforecast/imgs_models/dlinear.png" />

  <figcaption aria-hidden="true">Figure 1. DLinear
  Architecture.</figcaption>
</figure>

## 1. Auxiliary Functions

***

<a href="https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/models/dlinear.py#L36" target="_blank" style={{ float: "right", fontSize: "smaller" }}>source</a>

### SeriesDecomp

> ```text theme={null}
>  SeriesDecomp (kernel_size)
> ```

*Series decomposition block*

***

<a href="https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/models/dlinear.py#L17" target="_blank" style={{ float: "right", fontSize: "smaller" }}>source</a>

### MovingAvg

> ```text theme={null}
>  MovingAvg (kernel_size, stride)
> ```

*Moving average block to highlight the trend of time series*

## 2. DLinear

***

<a href="https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/models/dlinear.py#L51" target="_blank" style={{ float: "right", fontSize: "smaller" }}>source</a>

### DLinear

> ```text theme={null}
>  DLinear (h:int, input_size:int, stat_exog_list=None, hist_exog_list=None,
>           futr_exog_list=None, exclude_insample_y=False,
>           moving_avg_window:int=25, loss=MAE(), valid_loss=None,
>           max_steps:int=5000, learning_rate:float=0.0001,
>           num_lr_decays:int=-1, early_stop_patience_steps:int=-1,
>           val_check_steps:int=100, batch_size:int=32,
>           valid_batch_size:Optional[int]=None, windows_batch_size=1024,
>           inference_windows_batch_size=1024, start_padding_enabled=False,
>           step_size:int=1, scaler_type:str='identity', random_seed:int=1,
>           drop_last_loader:bool=False, alias:Optional[str]=None,
>           optimizer=None, optimizer_kwargs=None, lr_scheduler=None,
>           lr_scheduler_kwargs=None, dataloader_kwargs=None,
>           **trainer_kwargs)
> ```

\*DLinear

*Parameters:*<br /> `h`: int, forecast horizon.<br /> `input_size`: int,
maximum sequence length for truncated train backpropagation. <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 /> `moving_avg_window`: int=25,
window size for trend-seasonality decomposition. Should be uneven.<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=1024, number of windows to sample in
each inference batch.<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=‘robust’, type of scaler for temporal
inputs normalization see [temporal
scalers](https://nixtla.github.io/neuralforecast/common.scalers.html).<br />
`random_seed`: int=1, 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 />

```text theme={null}
*References*<br/>
- Zeng, Ailing, et al. "Are transformers effective for time series forecasting?." Proceedings of the AAAI conference on artificial intelligence. Vol. 37. No. 9. 2023."*
```

***

### DLinear.fit

> ```text theme={null}
>  DLinear.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 />\*

***

### DLinear.predict

> ```text theme={null}
>  DLinear.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 DLinear
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic, augment_calendar_df

AirPassengersPanel, calendar_cols = augment_calendar_df(df=AirPassengersPanel, freq='M')

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

model = DLinear(h=12,
                 input_size=24,
                 loss=MAE(),
                 scaler_type='robust',
                 learning_rate=1e-3,
                 max_steps=500,
                 val_check_steps=50,
                 early_stop_patience_steps=2)

nf = NeuralForecast(
    models=[model],
    freq='ME'
)
nf.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)
forecasts = nf.predict(futr_df=Y_test_df)

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])

if model.loss.is_distribution_output:
    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['DLinear-median'], c='blue', label='median')
    plt.fill_between(x=plot_df['ds'][-12:], 
                    y1=plot_df['DLinear-lo-90'][-12:].values, 
                    y2=plot_df['DLinear-hi-90'][-12:].values,
                    alpha=0.4, label='level 90')
    plt.grid()
    plt.legend()
    plt.plot()
else:
    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['DLinear'], c='blue', label='Forecast')
    plt.legend()
    plt.grid()
```