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

> Autoformer: Transformer with auto-correlation mechanism and progressive decomposition for reliable long-horizon time series forecasting with trend-seasonality.

# Autoformer

The Autoformer model tackles the challenge of finding reliable
dependencies on intricate temporal patterns of long-horizon forecasting.

The architecture has the following distinctive features: - In-built
progressive decomposition in trend and seasonal compontents based on a
moving average filter. - Auto-Correlation mechanism that discovers the
period-based dependencies by calculating the autocorrelation and
aggregating similar sub-series based on the periodicity. - Classic
encoder-decoder proposed by Vaswani et al. (2017) with a multi-head
attention mechanism.

The Autoformer model utilizes a three-component approach to define its
embedding: - It employs encoded autoregressive features obtained from a
convolution network. - Absolute positional embeddings obtained from
calendar features are utilized.

**References**

* [Wu, Haixu, Jiehui Xu, Jianmin Wang, and Mingsheng
  Long. “Autoformer: Decomposition transformers with auto-correlation for
  long-term series
  forecasting”](https://proceedings.neurips.cc/paper/2021/hash/bcc0d400288793e8bdcd7c19a8ac0c2b-Abstract.html)

<img src="https://mintcdn.com/nixtla/ldwvWbCUC65OBWwN/neuralforecast/imgs_models/autoformer.png?fit=max&auto=format&n=ldwvWbCUC65OBWwN&q=85&s=86a9843007f3018d1ff9b0b1b8775f1b" alt="Figure 1. Autoformer Architecture." width="1878" height="780" data-path="neuralforecast/imgs_models/autoformer.png" />

*Figure 1. Autoformer
Architecture.*

## 1. Autoformer

### `Autoformer`

```python theme={null}
Autoformer(
    h,
    input_size,
    stat_exog_list=None,
    hist_exog_list=None,
    futr_exog_list=None,
    cat_exog_list=None,
    categorical_cardinalities=None,
    cat_emb_dim="fastai",
    exclude_insample_y=False,
    decoder_input_size_multiplier=0.5,
    hidden_size=128,
    dropout=0.05,
    factor=3,
    n_head=4,
    conv_hidden_size=32,
    activation="gelu",
    encoder_layers=2,
    decoder_layers=1,
    MovingAvg_window=25,
    loss=MAE(),
    valid_loss=None,
    max_steps=5000,
    learning_rate=0.0001,
    num_lr_decays=-1,
    early_stop_patience_steps=-1,
    val_monitor="ptl/val_loss",
    val_check_steps=100,
    batch_size=32,
    valid_batch_size=None,
    windows_batch_size=1024,
    inference_windows_batch_size=1024,
    start_padding_enabled=False,
    training_data_availability_threshold=0.0,
    step_size=1,
    scaler_type="identity",
    random_seed=1,
    drop_last_loader=False,
    alias=None,
    optimizer=None,
    optimizer_kwargs=None,
    lr_scheduler=None,
    lr_scheduler_kwargs=None,
    dataloader_kwargs=None,
    **trainer_kwargs
)
```

Bases: <code>[BaseModel](#neuralforecast.common._base_model.BaseModel)</code>

Autoformer

The Autoformer model tackles the challenge of finding reliable dependencies on intricate temporal patterns of long-horizon forecasting.

The architecture has the following distinctive features:

* In-built progressive decomposition in trend and seasonal components based on a moving average filter.
* Auto-Correlation mechanism that discovers the period-based dependencies by
  calculating the autocorrelation and aggregating similar sub-series based on the periodicity.
* Classic encoder-decoder proposed by Vaswani et al. (2017) with a multi-head attention mechanism.

The Autoformer model utilizes a three-component approach to define its embedding:

* It employs encoded autoregressive features obtained from a convolution network.
* Absolute positional embeddings obtained from calendar features are utilized.

**Parameters:**

| Name | Type | Description | Default |
| - | - | - | - |
| `h` | <code>[int](#int)</code> | forecast horizon. | *required* |
| `input_size` | <code>[int](#int)</code> | maximum sequence length for truncated train backpropagation. Default -1 uses all history. | *required* |
| `futr_exog_list` | <code>str list</code> | future exogenous columns. | <code>None</code> |
| `hist_exog_list` | <code>str list</code> | historic exogenous columns. | <code>None</code> |
| `stat_exog_list` | <code>str list</code> | static exogenous columns. | <code>None</code> |
| `cat_exog_list` | <code>str list</code> | exogenous columns (from `hist_exog_list` / `futr_exog_list`) to embed instead of scale. | <code>None</code> |
| `categorical_cardinalities` | <code>[dict](#dict)</code> | mapping from each categorical column to its number of distinct categories. | <code>None</code> |
| `cat_emb_dim` | <code>[str](#str) or [int](#int)</code> | categorical embedding size strategy ('fastai', 'sqrt', 'half') or an explicit integer. | <code>'fastai'</code> |
| `exclude_insample_y` | <code>[bool](#bool)</code> | the model skips the autoregressive features y\[t-input\_size:t] if True. | <code>False</code> |
| `decoder_input_size_multiplier` | <code>[float](#float)</code> | . | <code>0.5</code> |
| `hidden_size` | <code>[int](#int)</code> | units of embeddings and encoders. | <code>128</code> |
| `n_head` | <code>[int](#int)</code> | controls number of multi-head's attention. | <code>4</code> |
| `dropout` | <code>[float](#float)</code> | dropout throughout Autoformer architecture. | <code>0.05</code> |
| `factor` | <code>[int](#int)</code> | Probsparse attention factor. | <code>3</code> |
| `conv_hidden_size` | <code>[int](#int)</code> | channels of the convolutional encoder. | <code>32</code> |
| `activation` | <code>[str](#str)</code> | activation from \['ReLU', 'Softplus', 'Tanh', 'SELU', 'LeakyReLU', 'PReLU', 'Sigmoid', 'GELU']. | <code>'gelu'</code> |
| `encoder_layers` | <code>[int](#int)</code> | number of layers for the TCN encoder. | <code>2</code> |
| `decoder_layers` | <code>[int](#int)</code> | number of layers for the MLP decoder. | <code>1</code> |
| `MovingAvg_window` | <code>[int](#int)</code> | window size for the moving average filter. | <code>25</code> |
| `loss` | <code>PyTorch module</code> | instantiated train loss class from [losses collection](./losses.pytorch.html). | <code>[MAE](#neuralforecast.losses.pytorch.MAE)()</code> |
| `valid_loss` | <code>PyTorch module</code> | instantiated validation loss class from [losses collection](./losses.pytorch.html). | <code>None</code> |
| `max_steps` | <code>[int](#int)</code> | maximum number of training steps. | <code>5000</code> |
| `learning_rate` | <code>[float](#float)</code> | Learning rate between (0, 1). | <code>0.0001</code> |
| `num_lr_decays` | <code>[int](#int)</code> | Number of learning rate decays, evenly distributed across max\_steps. | <code>-1</code> |
| `early_stop_patience_steps` | <code>[int](#int)</code> | Number of validation iterations before early stopping. | <code>-1</code> |
| `val_monitor` | <code>[str](#str)</code> | metric to monitor for early stopping. Valid options: "ptl/val\_loss", "valid\_loss", "train\_loss". Default: "ptl/val\_loss". | <code>'ptl/val\_loss'</code> |
| `val_check_steps` | <code>[int](#int)</code> | Number of training steps between every validation loss check. | <code>100</code> |
| `batch_size` | <code>[int](#int)</code> | number of different series in each batch. | <code>32</code> |
| `valid_batch_size` | <code>[int](#int)</code> | number of different series in each validation and test batch, if None uses batch\_size. | <code>None</code> |
| `windows_batch_size` | <code>[int](#int)</code> | number of windows to sample in each training batch, default uses all. | <code>1024</code> |
| `inference_windows_batch_size` | <code>[int](#int)</code> | number of windows to sample in each inference batch. | <code>1024</code> |
| `start_padding_enabled` | <code>[bool](#bool)</code> | if True, the model will pad the time series with zeros at the beginning, by input size. | <code>False</code> |
| `training_data_availability_threshold` | <code>[Union](#Union)\[[float](#float), [List](#List)\[[float](#float)]]</code> | minimum fraction of valid data points required for training windows. Single float applies to both insample and outsample; list of two floats specifies \[insample\_fraction, outsample\_fraction]. Default 0.0 allows windows with only 1 valid data point (current behavior). | <code>0.0</code> |
| `step_size` | <code>[int](#int)</code> | step size between each window of temporal data. | <code>1</code> |
| `scaler_type` | <code>[str](#str)</code> | type of scaler for temporal inputs normalization see [temporal scalers](https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/common/_scalers.py). | <code>'identity'</code> |
| `random_seed` | <code>[int](#int)</code> | random\_seed for pytorch initializer and numpy generators. | <code>1</code> |
| `drop_last_loader` | <code>[bool](#bool)</code> | if True `TimeSeriesDataLoader` drops last non-full batch. | <code>False</code> |
| `alias` | <code>[str](#str)</code> | optional, Custom name of the model. | <code>None</code> |
| `optimizer` | <code>Subclass of 'torch.optim.Optimizer'</code> | optional, user specified optimizer instead of the default choice (Adam). | <code>None</code> |
| `optimizer_kwargs` | <code>[dict](#dict)</code> | optional, list of parameters used by the user specified `optimizer`. | <code>None</code> |
| `lr_scheduler` | <code>Subclass of 'torch.optim.lr\_scheduler.LRScheduler'</code> | optional, user specified lr\_scheduler instead of the default choice (StepLR). | <code>None</code> |
| `lr_scheduler_kwargs` | <code>[dict](#dict)</code> | optional, list of parameters used by the user specified `lr_scheduler`. | <code>None</code> |
| `dataloader_kwargs` | <code>[dict](#dict)</code> | optional, list of parameters passed into the PyTorch Lightning dataloader by the `TimeSeriesDataLoader`. | <code>None</code> |
| `**trainer_kwargs` | <code>[int](#int)</code> | keyword trainer arguments inherited from [PyTorch Lightning's trainer](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer). | <code>{}</code> |

<details class="references" open markdown="1">
  <summary>References</summary>

  * [Wu, Haixu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. "Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting"](https://proceedings.neurips.cc/paper/2021/hash/bcc0d400288793e8bdcd7c19a8ac0c2b-Abstract.html)
</details>

#### `Autoformer.fit`

```python theme={null}
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:**

| Name | Type | Description | Default |
| - | - | - | - |
| `dataset` | <code>[TimeSeriesDataset](#TimeSeriesDataset)</code> | NeuralForecast's `TimeSeriesDataset`, see [documentation](./tsdataset.html). | *required* |
| `val_size` | <code>[int](#int)</code> | Validation size for temporal cross-validation. | <code>0</code> |
| `random_seed` | <code>[int](#int)</code> | Random seed for pytorch initializer and numpy generators, overwrites model.**init**'s. | <code>None</code> |
| `test_size` | <code>[int](#int)</code> | Test size for temporal cross-validation. | <code>0</code> |

**Returns:**

| Type | Description |
| - | - |
| None | |

#### `Autoformer.predict`

```python theme={null}
predict(
    dataset,
    test_size=None,
    step_size=1,
    random_seed=None,
    quantiles=None,
    h=None,
    explainer_config=None,
    **data_module_kwargs
)
```

Predict.

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

**Parameters:**

| Name | Type | Description | Default |
| - | - | - | - |
| `dataset` | <code>[TimeSeriesDataset](#TimeSeriesDataset)</code> | NeuralForecast's `TimeSeriesDataset`, see [documentation](./tsdataset.html). | *required* |
| `test_size` | <code>[int](#int)</code> | Test size for temporal cross-validation. | <code>None</code> |
| `step_size` | <code>[int](#int)</code> | Step size between each window. | <code>1</code> |
| `random_seed` | <code>[int](#int)</code> | Random seed for pytorch initializer and numpy generators, overwrites model.**init**'s. | <code>None</code> |
| `quantiles` | <code>[list](#list)</code> | Target quantiles to predict. | <code>None</code> |
| `h` | <code>[int](#int)</code> | Prediction horizon, if None, uses the model's fitted horizon. Defaults to None. | <code>None</code> |
| `explainer_config` | <code>[dict](#dict)</code> | configuration for explanations. | <code>None</code> |
| `**data_module_kwargs` | <code>[dict](#dict)</code> | PL's TimeSeriesDataModule args, see [documentation](https://pytorch-lightning.readthedocs.io/en/1.6.1/extensions/datamodules.html#using-a-datamodule). | <code>{}</code> |

**Returns:**

| Type | Description |
| - | - |
| None | |

### Usage Example

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

from neuralforecast import NeuralForecast
from neuralforecast.models import Autoformer
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 = Autoformer(h=12,
                 input_size=24,
                 hidden_size = 16,
                 conv_hidden_size = 32,
                 n_head=2,
                 loss=MAE(),
                 futr_exog_list=calendar_cols,
                 scaler_type='robust',
                 learning_rate=1e-3,
                 max_steps=300,
                 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['Autoformer-median'], c='blue', label='median')
    plt.fill_between(x=plot_df['ds'][-12:], 
                    y1=plot_df['Autoformer-lo-90'][-12:].values, 
                    y2=plot_df['Autoformer-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['Autoformer'], c='blue', label='Forecast')
    plt.legend()
    plt.grid()
```

## 2. Auxiliary functions

### `Decoder`

```python theme={null}
Decoder(layers, norm_layer=None, projection=None)
```

Bases: <code>[Module](#torch.nn.Module)</code>

Autoformer decoder

### `DecoderLayer`

```python theme={null}
DecoderLayer(
    self_attention,
    cross_attention,
    hidden_size,
    c_out,
    conv_hidden_size=None,
    MovingAvg=25,
    dropout=0.1,
    activation="relu",
)
```

Bases: <code>[Module](#torch.nn.Module)</code>

Autoformer decoder layer with the progressive decomposition architecture

### `Encoder`

```python theme={null}
Encoder(attn_layers, conv_layers=None, norm_layer=None)
```

Bases: <code>[Module](#torch.nn.Module)</code>

Autoformer encoder

### `EncoderLayer`

```python theme={null}
EncoderLayer(
    attention,
    hidden_size,
    conv_hidden_size=None,
    MovingAvg=25,
    dropout=0.1,
    activation="relu",
)
```

Bases: <code>[Module](#torch.nn.Module)</code>

Autoformer encoder layer with the progressive decomposition architecture

### `LayerNorm`

```python theme={null}
LayerNorm(channels)
```

Bases: <code>[Module](#torch.nn.Module)</code>

Special designed layernorm for the seasonal part

### `AutoCorrelationLayer`

```python theme={null}
AutoCorrelationLayer(
    correlation, hidden_size, n_head, d_keys=None, d_values=None
)
```

Bases: <code>[Module](#torch.nn.Module)</code>

Auto Correlation Layer

### `AutoCorrelation`

```python theme={null}
AutoCorrelation(
    mask_flag=True,
    factor=1,
    scale=None,
    attention_dropout=0.1,
    output_attention=False,
)
```

Bases: <code>[Module](#torch.nn.Module)</code>

AutoCorrelation Mechanism with the following two phases:
(1) period-based dependencies discovery
(2) time delay aggregation
This block can replace the self-attention family mechanism seamlessly.


## Related topics

- [Long Horizon](/datasetsforecast/long_horizon.html.md)
- [Long-Horizon Original Datasets](/datasetsforecast/long_horizon2.html.md)
- [Long-Horizon Forecasting with NHITS](/neuralforecast/docs/tutorials/longhorizon_nhits.html.md)
- [Automatic Forecasting](/neuralforecast/models.html.md)
- [Long-Horizon Forecasting with Transformer models](/neuralforecast/docs/tutorials/longhorizon_transformers.html.md)