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
- Zeng, Ailing, et al. “Are transformers effective for time series forecasting?.” Proceedings of the AAAI conference on artificial intelligence. Vol. 37. No. 9. 2023.”

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1. Auxiliary Functions

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SeriesDecomp

 SeriesDecomp (kernel_size)

Series decomposition block

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MovingAvg

 MovingAvg (kernel_size, stride)

Moving average block to highlight the trend of time series

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2. DLinear

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DLinear

 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:
h: int, forecast horizon.
input_size: int, maximum sequence length for truncated train backpropagation.
stat_exog_list: str list, static exogenous columns.
hist_exog_list: str list, historic exogenous columns.
futr_exog_list: str list, future exogenous columns.
exclude_insample_y: bool=False, the model skips the autoregressive features y[t-input_size:t] if True.
moving_avg_window: int=25, window size for trend-seasonality decomposition. Should be uneven.
loss: PyTorch module, instantiated train loss class from losses collection.
valid_loss: PyTorch module=loss, instantiated valid loss class from losses collection.
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=1024, number of windows to sample in each inference batch.
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=‘robust’, type of scaler for temporal inputs normalization see temporal scalers.
random_seed: int=1, 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.

*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."*

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DLinear.fit

 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.

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, see documentation.
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.
*

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DLinear.predict

 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:
dataset: NeuralForecast’s TimeSeriesDataset, see documentation.
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.*

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Usage Example

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()