Forecasting Model Base Classes

A forecasting model captures the future values of a time series as a function of the past as follows:

\[y_{t+1} = f(y_t, y_{t-1}, ..., y_1),\]

where \(y_t\) represents the time series’ value(s) at time \(t\).

The main functions are fit() and predict(). fit() learns the function f(), over the history of one or several time series. The function predict() applies f() on one or several time series in order to obtain forecasts for a desired number of time stamps into the future.

class darts.models.forecasting.forecasting_model.ForecastingModel(*args, **kwargs)

Bases: ABC

The base class for forecasting models. It defines the minimal behavior that all forecasting models have to support. The signatures in this base class are for “local” models handling only one univariate series and no covariates. Sub-classes can handle more complex cases.

Attributes

considers_static_covariates	Whether the model considers static covariates, if there are any.
extreme_lags	A 8-tuple containing in order: (min target lag, max target lag, min past covariate lag, max past covariate lag, min future covariate lag, max future covariate lag, output shift, max target lag train (only for RNNModel)).
min_train_samples	The minimum number of samples for training the model.
output_chunk_length	Number of time steps predicted at once by the model, not defined for statistical models.
output_chunk_shift	Number of time steps that the output/prediction starts after the end of the input.
supports_future_covariates	Whether model supports future covariates
supports_likelihood_parameter_prediction	Whether model instance supports direct prediction of likelihood parameters
supports_multivariate	Whether the model considers more than one variate in the time series.
supports_optimized_historical_forecasts	Whether the model supports optimized historical forecasts
supports_past_covariates	Whether model supports past covariates
supports_probabilistic_prediction	Checks if the forecasting model with this configuration supports probabilistic predictions.
supports_sample_weight	Whether model supports sample weight for training.
supports_static_covariates	Whether model supports static covariates
supports_transferrable_series_prediction	Whether the model supports prediction for any input series.
uses_future_covariates	Whether the model uses future covariates, once fitted.
uses_past_covariates	Whether the model uses past covariates, once fitted.
uses_static_covariates	Whether the model uses static covariates, once fitted.

model_params

Methods

backtest(series[, past_covariates, ...])	Compute error values that the model produced for historical forecasts on (potentially multiple) series.
fit(series)	Fit/train the model on the provided series.
generate_fit_encodings(series[, ...])	Generates the covariate encodings that were used/generated for fitting the model and returns a tuple of past, and future covariates series with the original and encoded covariates stacked together.
generate_fit_predict_encodings(n, series[, ...])	Generates covariate encodings for training and inference/prediction and returns a tuple of past, and future covariates series with the original and encoded covariates stacked together.
generate_predict_encodings(n, series[, ...])	Generates covariate encodings for the inference/prediction set and returns a tuple of past, and future covariates series with the original and encoded covariates stacked together.
gridsearch(parameters, series[, ...])	Find the best hyper-parameters among a given set using a grid search.
historical_forecasts(series[, ...])	Generates historical forecasts by simulating predictions at various points in time throughout the history of the provided (potentially multiple) series.
load(path)	Loads the model from a given path or file handle.
predict(n[, num_samples, verbose, show_warnings])	Forecasts values for n time steps after the end of the training series.
residuals(series[, past_covariates, ...])	Compute the residuals that the model produced for historical forecasts on (potentially multiple) series.
save([path])	Saves the model under a given path or file handle.

backtest(series, past_covariates=None, future_covariates=None, historical_forecasts=None, forecast_horizon=1, num_samples=1, train_length=None, start=None, start_format='value', stride=1, retrain=True, overlap_end=False, last_points_only=False, metric=<function mape>, reduction=<function mean>, verbose=False, show_warnings=True, predict_likelihood_parameters=False, enable_optimization=True, data_transformers=None, metric_kwargs=None, fit_kwargs=None, predict_kwargs=None, sample_weight=None)

Compute error values that the model produced for historical forecasts on (potentially multiple) series.

If historical_forecasts are provided, the metric(s) (given by the metric function) is evaluated directly on all forecasts and actual values. The same series and last_points_only value must be passed that were used to generate the historical forecasts. Finally, the method returns an optional reduction (the mean by default) of all these metric scores.

If historical_forecasts is None, it first generates the historical forecasts with the parameters given below (see ForecastingModel.historical_forecasts() for more info) and then evaluates as described above.

The metric(s) can be further customized metric_kwargs (e.g. control the aggregation over components, time steps, multiple series, other required arguments such as q for quantile metrics, …).

Parameters

• series (Union[TimeSeries, Sequence[TimeSeries]]) – A (sequence of) target time series used to successively train (if retrain is not False) and compute the historical forecasts.

• past_covariates (Union[TimeSeries, Sequence[TimeSeries], None]) – Optionally, a (sequence of) past-observed covariate time series for every input time series in series. This applies only if the model supports past covariates.

• future_covariates (Union[TimeSeries, Sequence[TimeSeries], None]) – Optionally, a (sequence of) future-known covariate time series for every input time series in series. This applies only if the model supports future covariates.

• historical_forecasts (Union[TimeSeries, Sequence[TimeSeries], Sequence[Sequence[TimeSeries]], None]) – Optionally, the (or a sequence of / a sequence of sequences of) historical forecasts time series to be evaluated. Corresponds to the output of historical_forecasts(). The same series and last_points_only values must be passed that were used to generate the historical forecasts. If provided, will skip historical forecasting and ignore all parameters except series, last_points_only, metric, and reduction.

• forecast_horizon (int) – The forecast horizon for the predictions.

• num_samples (int) – Number of times a prediction is sampled from a probabilistic model. Use values >1 only for probabilistic models.

• train_length (Optional[int, None]) – Optionally, use a fixed length / number of time steps for every constructed training set (rolling window mode). Only effective when retrain is not False. The default is None, where it uses all time steps up until the prediction time (expanding window mode). If larger than the number of available time steps, uses the expanding mode. Needs to be at least min_train_series_length.

• start (Union[Timestamp, float, int, None]) –

  Optionally, the first point in time at which a prediction is computed. This parameter supports: float, int, pandas.Timestamp, and None. If a float, it is the proportion of the time series that should lie before the first prediction point. If an int, it is either the index position of the first prediction point for series with a pd.DatetimeIndex, or the index value for series with a pd.RangeIndex. The latter can be changed to the index position with start_format=”position”. If a pandas.Timestamp, it is the time stamp of the first prediction point. If None, the first prediction point will automatically be set to:

  • the first predictable point if retrain is False, or retrain is a Callable and the first predictable point is earlier than the first trainable point.

  • the first trainable point if retrain is True or int (given train_length), or retrain is a Callable and the first trainable point is earlier than the first predictable point.

  • the first trainable point (given train_length) otherwise

  Note: If start is not within the trainable / forecastable points, uses the closest valid start point that

  is a round multiple of stride ahead of start. Raises a ValueError, if no valid start point exists.

  Note: If the model uses a shifted output (output_chunk_shift > 0), then the first predicted point is also

  shifted by output_chunk_shift points into the future.

  Note: If start is outside the possible historical forecasting times, will ignore the parameter

  (default behavior with None) and start at the first trainable/predictable point.

• start_format (Literal[‘position’, ‘value’]) – Defines the start format. If set to 'position', start corresponds to the index position of the first predicted point and can range from (-len(series), len(series) - 1). If set to 'value', start corresponds to the index value/label of the first predicted point. Will raise an error if the value is not in series’ index. Default: 'value'.

• stride (int) – The number of time steps between two consecutive predictions.

• retrain (Union[bool, int, Callable[…, bool]]) –

  Whether and/or on which condition to retrain the model before predicting. This parameter supports 3 different types: bool, (positive) int, and Callable (returning a bool). In the case of bool: retrain the model at each step (True), or never retrain the model (False). In the case of int: the model is retrained every retrain iterations. In the case of Callable: the model is retrained whenever callable returns True. The callable must have the following positional arguments:

  • counter (int): current retrain iteration

  • pred_time (pd.Timestamp or int): timestamp of forecast time (end of the training series)

  • train_series (TimeSeries): train series up to pred_time

  • past_covariates (TimeSeries): past_covariates series up to pred_time

  • future_covariates (TimeSeries): future_covariates series up to min(pred_time + series.freq * forecast_horizon, series.end_time())

  Note: if any optional *_covariates are not passed to historical_forecast, None will be passed to the corresponding retrain function argument. Note: some models require being retrained every time and do not support anything other than retrain=True. Note: also controls the retraining of the data_transformers.

• overlap_end (bool) – Whether the returned forecasts can go beyond the series’ end or not.

• last_points_only (bool) – Whether to return only the last point of each historical forecast. If set to True, the method returns a single TimeSeries (for each time series in series) containing the successive point forecasts. Otherwise, returns a list of historical TimeSeries forecasts.

• metric (Union[Callable[…, Union[float, list[float], ndarray, list[ndarray]]], list[Callable[…, Union[float, list[float], ndarray, list[ndarray]]]]]) – A metric function or a list of metric functions. Each metric must either be a Darts metric (see here), or a custom metric that has an identical signature as Darts’ metrics, uses decorators multi_ts_support() and multi_ts_support(), and returns the metric score.

• reduction (Optional[Callable[…, float], None]) – A function used to combine the individual error scores obtained when last_points_only is set to False. When providing several metric functions, the function will receive the argument axis = 1 to obtain single value for each metric function. If explicitly set to None, the method will return a list of the individual error scores instead. Set to np.mean by default.

• verbose (bool) – Whether to print the progress.

• show_warnings (bool) – Whether to show warnings related to historical forecasts optimization, or parameters start and train_length.

• predict_likelihood_parameters (bool) – If set to True, the model predicts the parameters of its likelihood instead of the target. Only supported for probabilistic models with a likelihood, num_samples = 1 and n<=output_chunk_length. Default: False.

• enable_optimization (bool) – Whether to use the optimized version of historical_forecasts when supported and available. Default: True.

• data_transformers (Optional[dict[str, Union[BaseDataTransformer, Pipeline]], None]) –

  Optionally, a dictionary of BaseDataTransformer or Pipeline to apply to the corresponding series (possibles keys; “series”, “past_covariates”, “future_covariates”). If provided, all input series must be in the un-transformed space. For fittable transformer / pipeline:

  • if retrain=True, the data transformer re-fit on the training data at each historical forecast step.

  • if retrain=False, the data transformer transforms the series once before all the forecasts.

  The fitted transformer is used to transform the input during both training and prediction. If the transformation is invertible, the forecasts will be inverse-transformed. Only effective when historical_forecasts=None.

• metric_kwargs (Union[dict[str, Any], list[dict[str, Any]], None]) – Additional arguments passed to metric(), such as ‘n_jobs’ for parallelization, ‘component_reduction’ for reducing the component wise metrics, seasonality ‘m’ for scaled metrics, etc. Will pass arguments to each metric separately and only if they are present in the corresponding metric signature. Parameter ‘insample’ for scaled metrics (e.g. mase`, rmsse, …) is ignored, as it is handled internally.

• fit_kwargs (Optional[dict[str, Any], None]) – Optionally, some additional arguments passed to the model fit() method.

• predict_kwargs (Optional[dict[str, Any], None]) – Optionally, some additional arguments passed to the model predict() method.

• sample_weight (Union[TimeSeries, Sequence[TimeSeries], str, None]) – Optionally, some sample weights to apply to the target series labels for training. Only effective when retrain is not False. They are applied per observation, per label (each step in output_chunk_length), and per component. If a series or sequence of series, then those weights are used. If the weight series only have a single component / column, then the weights are applied globally to all components in series. Otherwise, for component-specific weights, the number of components must match those of series. If a string, then the weights are generated using built-in weighting functions. The available options are “linear” or “exponential” decay - the further in the past, the lower the weight. The weights are computed per time series.

Return type

Union[float, ndarray, list[float], list[ndarray]]

Returns

• float – A single backtest score for single uni/multivariate series, a single metric function and:

  • historical_forecasts generated with last_points_only=True

  • historical_forecasts generated with last_points_only=False and using a backtest reduction

• np.ndarray – An numpy array of backtest scores. For single series and one of:

  • a single metric function, historical_forecasts generated with last_points_only=False and backtest reduction=None. The output has shape (n forecasts, *).

  • multiple metric functions and historical_forecasts generated with last_points_only=False. The output has shape (*, n metrics) when using a backtest reduction, and (n forecasts, *, n metrics) when reduction=None

  • multiple uni/multivariate series including series_reduction and at least one of component_reduction=None or time_reduction=None for “per time step metrics”

• List[float] – Same as for type float but for a sequence of series. The returned metric list has length len(series) with the float metric for each input series.

• List[np.ndarray] – Same as for type np.ndarray but for a sequence of series. The returned metric list has length len(series) with the np.ndarray metrics for each input series.

property considers_static_covariates: bool

Whether the model considers static covariates, if there are any.

Return type

bool

abstract property extreme_lags: tuple[Optional[int], Optional[int], Optional[int], Optional[int], Optional[int], Optional[int], int, Optional[int]]

A 8-tuple containing in order: (min target lag, max target lag, min past covariate lag, max past covariate lag, min future covariate lag, max future covariate lag, output shift, max target lag train (only for RNNModel)). If 0 is the index of the first prediction, then all lags are relative to this index.

See examples below.

If the model wasn’t fitted with:

• target (concerning RegressionModels only): then the first element should be None.

• past covariates: then the third and fourth elements should be None.

• future covariates: then the fifth and sixth elements should be None.

Should be overridden by models that use past or future covariates, and/or for model that have minimum target lag and maximum target lags potentially different from -1 and 0.

Notes

maximum target lag (second value) cannot be None and is always larger than or equal to 0.

Examples

>>> model = LinearRegressionModel(lags=3, output_chunk_length=2)
>>> model.fit(train_series)
>>> model.extreme_lags
(-3, 1, None, None, None, None, 0, None)
>>> model = LinearRegressionModel(lags=3, output_chunk_length=2, output_chunk_shift=2)
>>> model.fit(train_series)
>>> model.extreme_lags
(-3, 1, None, None, None, None, 2, None)
>>> model = LinearRegressionModel(lags=[-3, -5], lags_past_covariates = 4, output_chunk_length=7)
>>> model.fit(train_series, past_covariates=past_covariates)
>>> model.extreme_lags
(-5, 6, -4, -1,  None, None, 0, None)
>>> model = LinearRegressionModel(lags=[3, 5], lags_future_covariates = [4, 6], output_chunk_length=7)
>>> model.fit(train_series, future_covariates=future_covariates)
>>> model.extreme_lags
(-5, 6, None, None, 4, 6, 0, None)
>>> model = NBEATSModel(input_chunk_length=10, output_chunk_length=7)
>>> model.fit(train_series)
>>> model.extreme_lags
(-10, 6, None, None, None, None, 0, None)
>>> model = NBEATSModel(input_chunk_length=10, output_chunk_length=7, lags_future_covariates=[4, 6])
>>> model.fit(train_series, future_covariates)
>>> model.extreme_lags
(-10, 6, None, None, 4, 6, 0, None)

Return type

tuple[Optional[int, None], Optional[int, None], Optional[int, None], Optional[int, None], Optional[int, None], Optional[int, None], int, Optional[int, None]]

abstract fit(series)

Fit/train the model on the provided series.

Parameters

series (TimeSeries) – A target time series. The model will be trained to forecast this time series.

Returns

Fitted model.

Return type

self

generate_fit_encodings(series, past_covariates=None, future_covariates=None)

Generates the covariate encodings that were used/generated for fitting the model and returns a tuple of past, and future covariates series with the original and encoded covariates stacked together. The encodings are generated by the encoders defined at model creation with parameter add_encoders. Pass the same series, past_covariates, and future_covariates that you used to train/fit the model.

Parameters

• series (Union[TimeSeries, Sequence[TimeSeries]]) – The series or sequence of series with the target values used when fitting the model.

• past_covariates (Union[TimeSeries, Sequence[TimeSeries], None]) – Optionally, the series or sequence of series with the past-observed covariates used when fitting the model.

• future_covariates (Union[TimeSeries, Sequence[TimeSeries], None]) – Optionally, the series or sequence of series with the future-known covariates used when fitting the model.

Returns

A tuple of (past covariates, future covariates). Each covariate contains the original as well as the encoded covariates.

Return type

Tuple[Union[TimeSeries, Sequence[TimeSeries]], Union[TimeSeries, Sequence[TimeSeries]]]

generate_fit_predict_encodings(n, series, past_covariates=None, future_covariates=None)

Generates covariate encodings for training and inference/prediction and returns a tuple of past, and future covariates series with the original and encoded covariates stacked together. The encodings are generated by the encoders defined at model creation with parameter add_encoders. Pass the same series, past_covariates, and future_covariates that you intend to use for training and prediction.

Parameters

• n (int) – The number of prediction time steps after the end of series intended to be used for prediction.

• series (Union[TimeSeries, Sequence[TimeSeries]]) – The series or sequence of series with target values intended to be used for training and prediction.

• past_covariates (Union[TimeSeries, Sequence[TimeSeries], None]) – Optionally, the past-observed covariates series intended to be used for training and prediction. The dimensions must match those of the covariates used for training.

• future_covariates (Union[TimeSeries, Sequence[TimeSeries], None]) – Optionally, the future-known covariates series intended to be used for prediction. The dimensions must match those of the covariates used for training.

Returns

A tuple of (past covariates, future covariates). Each covariate contains the original as well as the encoded covariates.

Return type

Tuple[Union[TimeSeries, Sequence[TimeSeries]], Union[TimeSeries, Sequence[TimeSeries]]]

generate_predict_encodings(n, series, past_covariates=None, future_covariates=None)

Generates covariate encodings for the inference/prediction set and returns a tuple of past, and future covariates series with the original and encoded covariates stacked together. The encodings are generated by the encoders defined at model creation with parameter add_encoders. Pass the same series, past_covariates, and future_covariates that you intend to use for prediction.

Parameters

• n (int) – The number of prediction time steps after the end of series intended to be used for prediction.

• series (Union[TimeSeries, Sequence[TimeSeries]]) – The series or sequence of series with target values intended to be used for prediction.

• past_covariates (Union[TimeSeries, Sequence[TimeSeries], None]) – Optionally, the past-observed covariates series intended to be used for prediction. The dimensions must match those of the covariates used for training.

• future_covariates (Union[TimeSeries, Sequence[TimeSeries], None]) – Optionally, the future-known covariates series intended to be used for prediction. The dimensions must match those of the covariates used for training.

Returns

A tuple of (past covariates, future covariates). Each covariate contains the original as well as the encoded covariates.

Return type

Tuple[Union[TimeSeries, Sequence[TimeSeries]], Union[TimeSeries, Sequence[TimeSeries]]]

classmethod gridsearch(parameters, series, past_covariates=None, future_covariates=None, forecast_horizon=None, stride=1, start=None, start_format='value', last_points_only=False, show_warnings=True, val_series=None, use_fitted_values=False, metric=<function mape>, reduction=<function mean>, verbose=False, n_jobs=1, n_random_samples=None, data_transformers=None, fit_kwargs=None, predict_kwargs=None, sample_weight=None)

Find the best hyper-parameters among a given set using a grid search.

This function has 3 modes of operation: Expanding window mode, split mode and fitted value mode. The three modes of operation evaluate every possible combination of hyper-parameter values provided in the parameters dictionary by instantiating the model_class subclass of ForecastingModel with each combination, and returning the best-performing model with regard to the metric function. The metric function is expected to return an error value, thus the model resulting in the smallest metric output will be chosen.

The relationship of the training data and test data depends on the mode of operation.

Expanding window mode (activated when forecast_horizon is passed): For every hyperparameter combination, the model is repeatedly trained and evaluated on different splits of series. This process is accomplished by using the backtest() function as a subroutine to produce historic forecasts starting from start that are compared against the ground truth values of series. Note that the model is retrained for every single prediction, thus this mode is slower.

Split window mode (activated when val_series is passed): This mode will be used when the val_series argument is passed. For every hyper-parameter combination, the model is trained on series and evaluated on val_series.

Fitted value mode (activated when use_fitted_values is set to True): For every hyper-parameter combination, the model is trained on series and evaluated on the resulting fitted values. Not all models have fitted values, and this method raises an error if the model doesn’t have a fitted_values member. The fitted values are the result of the fit of the model on series. Comparing with the fitted values can be a quick way to assess the model, but one cannot see if the model is overfitting the series.

Derived classes must ensure that a single instance of a model will not share parameters with the other instances, e.g., saving models in the same path. Otherwise, an unexpected behavior can arise while running several models in parallel (when n_jobs != 1). If this cannot be avoided, then gridsearch should be redefined, forcing n_jobs = 1.

Currently this method only supports deterministic predictions (i.e. when models’ predictions have only 1 sample).

Parameters

• model_class – The ForecastingModel subclass to be tuned for ‘series’.

• parameters (dict) – A dictionary containing as keys hyperparameter names, and as values lists of values for the respective hyperparameter.

• series (TimeSeries) – The target series used as input and target for training.

• past_covariates (Optional[TimeSeries, None]) – Optionally, a past-observed covariate series. This applies only if the model supports past covariates.

• future_covariates (Optional[TimeSeries, None]) – Optionally, a future-known covariate series. This applies only if the model supports future covariates.

• forecast_horizon (Optional[int, None]) – The integer value of the forecasting horizon. Activates expanding window mode.

• stride (int) – Only used in expanding window mode. The number of time steps between two consecutive predictions.

• start (Union[Timestamp, float, int, None]) –

  Only used in expanding window mode. Optionally, the first point in time at which a prediction is computed. This parameter supports: float, int, pandas.Timestamp, and None. If a float, it is the proportion of the time series that should lie before the first prediction point. If an int, it is either the index position of the first prediction point for series with a pd.DatetimeIndex, or the index value for series with a pd.RangeIndex. The latter can be changed to the index position with start_format=”position”. If a pandas.Timestamp, it is the time stamp of the first prediction point. If None, the first prediction point will automatically be set to:

  • the first predictable point if retrain is False, or retrain is a Callable and the first predictable point is earlier than the first trainable point.

  • the first trainable point if retrain is True or int (given train_length), or retrain is a Callable and the first trainable point is earlier than the first predictable point.

  • the first trainable point (given train_length) otherwise

  Note: If start is not within the trainable / forecastable points, uses the closest valid start point that

  is a round multiple of stride ahead of start. Raises a ValueError, if no valid start point exists.

  Note: If the model uses a shifted output (output_chunk_shift > 0), then the first predicted point is also

  shifted by output_chunk_shift points into the future.

  Note: If start is outside the possible historical forecasting times, will ignore the parameter

  (default behavior with None) and start at the first trainable/predictable point.

• start_format (Literal[‘position’, ‘value’]) – Only used in expanding window mode. Defines the start format. Only effective when start is an integer and series is indexed with a pd.RangeIndex. If set to ‘position’, start corresponds to the index position of the first predicted point and can range from (-len(series), len(series) - 1). If set to ‘value’, start corresponds to the index value/label of the first predicted point. Will raise an error if the value is not in series’ index. Default: 'value'

• last_points_only (bool) – Only used in expanding window mode. Whether to use the whole forecasts or only the last point of each forecast to compute the error.

• show_warnings (bool) – Only used in expanding window mode. Whether to show warnings related to the start parameter.

• val_series (Optional[TimeSeries, None]) – The TimeSeries instance used for validation in split mode. If provided, this series must start right after the end of series; so that a proper comparison of the forecast can be made.

• use_fitted_values (bool) – If True, uses the comparison with the fitted values. Raises an error if fitted_values is not an attribute of model_class.

• metric (Callable[[TimeSeries, TimeSeries], float]) –

  A metric function that returns the error between two TimeSeries as a float value . Must either be one of Darts’ “aggregated over time” metrics (see here), or a custom metric that as input two TimeSeries and returns the error

• reduction (Callable[[ndarray], float]) – A reduction function (mapping array to float) describing how to aggregate the errors obtained on the different validation series when backtesting. By default it’ll compute the mean of errors.

• verbose – Whether to print the progress.

• n_jobs (int) – The number of jobs to run in parallel. Parallel jobs are created only when there are two or more parameters combinations to evaluate. Each job will instantiate, train, and evaluate a different instance of the model. Defaults to 1 (sequential). Setting the parameter to -1 means using all the available cores.

• n_random_samples (Union[int, float, None]) – The number/ratio of hyperparameter combinations to select from the full parameter grid. This will perform a random search instead of using the full grid. If an integer, n_random_samples is the number of parameter combinations selected from the full grid and must be between 0 and the total number of parameter combinations. If a float, n_random_samples is the ratio of parameter combinations selected from the full grid and must be between 0 and 1. Defaults to None, for which random selection will be ignored.

• data_transformers (Optional[dict[str, Union[BaseDataTransformer, Pipeline]], None]) –

  Optionally, a dictionary of BaseDataTransformer or Pipeline to apply to the corresponding series (possibles keys; “series”, “past_covariates”, “future_covariates”). If provided, all input series must be in the un-transformed space. For fittable transformer / pipeline:

  • if retrain=True, the data transformer re-fit on the training data at each historical forecast step.

  • if retrain=False, the data transformer transforms the series once before all the forecasts.

  The fitted transformer is used to transform the input during both training and prediction. If the transformation is invertible, the forecasts will be inverse-transformed.

• fit_kwargs (Optional[dict[str, Any], None]) – Additional arguments passed to the model fit() method.

• predict_kwargs (Optional[dict[str, Any], None]) – Additional arguments passed to the model predict() method.

• sample_weight (Union[TimeSeries, str, None]) – Optionally, some sample weights to apply to the target series labels for training. Only effective when retrain is not False. They are applied per observation, per label (each step in output_chunk_length), and per component. If a series, then those weights are used. If the weight series only have a single component / column, then the weights are applied globally to all components in series. Otherwise, for component-specific weights, the number of components must match those of series. If a string, then the weights are generated using built-in weighting functions. The available options are “linear” or “exponential” decay - the further in the past, the lower the weight.

Returns

A tuple containing an untrained model_class instance created from the best-performing hyper-parameters, along with a dictionary containing these best hyper-parameters, and metric score for the best hyper-parameters.

Return type

ForecastingModel, Dict, float

historical_forecasts(series, past_covariates=None, future_covariates=None, forecast_horizon=1, num_samples=1, train_length=None, start=None, start_format='value', stride=1, retrain=True, overlap_end=False, last_points_only=True, verbose=False, show_warnings=True, predict_likelihood_parameters=False, enable_optimization=True, data_transformers=None, fit_kwargs=None, predict_kwargs=None, sample_weight=None)

Generates historical forecasts by simulating predictions at various points in time throughout the history of the provided (potentially multiple) series. This process involves retrospectively applying the model to different time steps, as if the forecasts were made in real-time at those specific moments. This allows for an evaluation of the model’s performance over the entire duration of the series, providing insights into its predictive accuracy and robustness across different historical periods.

There are two main modes for this method:

• Re-training Mode (Default, retrain=True): The model is re-trained at each step of the simulation, and generates a forecast using the updated model. In case of multiple series, the model is re-trained on each series independently (global training is not yet supported).

• Pre-trained Mode (retrain=False): The forecasts are generated at each step of the simulation without re-training. It is only supported for pre-trained global forecasting models. This mode is significantly faster as it skips the re-training step.

By choosing the appropriate mode, you can balance between computational efficiency and the need for up-to-date model training.

Re-training Mode: This mode repeatedly builds a training set by either expanding from the beginning of the series or by using a fixed-length train_length (the start point can also be configured with start and start_format). The model is then trained on this training set, and a forecast of length forecast_horizon is generated. Subsequently, the end of the training set is moved forward by stride time steps, and the process is repeated.

Pre-trained Mode: This mode is only supported for pre-trained global forecasting models. It uses the same simulation steps as in the Re-training Mode (ignoring train_length), but generates the forecasts directly without re-training.

By default, with last_points_only=True, this method returns a single time series (or a sequence of time series) composed of the last point from each historical forecast. This time series will thus have a frequency of series.freq * stride. If last_points_only=False, it will instead return a list (or a sequence of lists) of the full historical forecast series each with frequency series.freq.

Parameters

• series (Union[TimeSeries, Sequence[TimeSeries]]) – A (sequence of) target time series used to successively train (if retrain is not False) and compute the historical forecasts.

• past_covariates (Union[TimeSeries, Sequence[TimeSeries], None]) – Optionally, a (sequence of) past-observed covariate time series for every input time series in series. This applies only if the model supports past covariates.

• future_covariates (Union[TimeSeries, Sequence[TimeSeries], None]) – Optionally, a (sequence of) future-known covariate time series for every input time series in series. This applies only if the model supports future covariates.

• forecast_horizon (int) – The forecast horizon for the predictions.

• num_samples (int) – Number of times a prediction is sampled from a probabilistic model. Use values >1 only for probabilistic models.

• train_length (Optional[int, None]) – Optionally, use a fixed length / number of time steps for every constructed training set (rolling window mode). Only effective when retrain is not False. The default is None, where it uses all time steps up until the prediction time (expanding window mode). If larger than the number of available time steps, uses the expanding mode. Needs to be at least min_train_series_length.

• start (Union[Timestamp, float, int, None]) –

  Optionally, the first point in time at which a prediction is computed. This parameter supports: float, int, pandas.Timestamp, and None. If a float, it is the proportion of the time series that should lie before the first prediction point. If an int, it is either the index position of the first prediction point for series with a pd.DatetimeIndex, or the index value for series with a pd.RangeIndex. The latter can be changed to the index position with start_format=”position”. If a pandas.Timestamp, it is the time stamp of the first prediction point. If None, the first prediction point will automatically be set to:

  • the first predictable point if retrain is False, or retrain is a Callable and the first predictable point is earlier than the first trainable point.

  • the first trainable point if retrain is True or int (given train_length), or retrain is a Callable and the first trainable point is earlier than the first predictable point.

  • the first trainable point (given train_length) otherwise

  Note: If start is not within the trainable / forecastable points, uses the closest valid start point that

  is a round multiple of stride ahead of start. Raises a ValueError, if no valid start point exists.

  Note: If the model uses a shifted output (output_chunk_shift > 0), then the first predicted point is also

  shifted by output_chunk_shift points into the future.

  Note: If start is outside the possible historical forecasting times, will ignore the parameter

  (default behavior with None) and start at the first trainable/predictable point.

• start_format (Literal[‘position’, ‘value’]) – Defines the start format. If set to 'position', start corresponds to the index position of the first predicted point and can range from (-len(series), len(series) - 1). If set to 'value', start corresponds to the index value/label of the first predicted point. Will raise an error if the value is not in series’ index. Default: 'value'.

• stride (int) – The number of time steps between two consecutive predictions.

• retrain (Union[bool, int, Callable[…, bool]]) –

  Whether and/or on which condition to retrain the model before predicting. This parameter supports 3 different types: bool, (positive) int, and Callable (returning a bool). In the case of bool: retrain the model at each step (True), or never retrain the model (False). In the case of int: the model is retrained every retrain iterations. In the case of Callable: the model is retrained whenever callable returns True. The callable must have the following positional arguments:

  • counter (int): current retrain iteration

  • pred_time (pd.Timestamp or int): timestamp of forecast time (end of the training series)

  • train_series (TimeSeries): train series up to pred_time

  • past_covariates (TimeSeries): past_covariates series up to pred_time

  • future_covariates (TimeSeries): future_covariates series up to min(pred_time + series.freq * forecast_horizon, series.end_time())

  Note: if any optional *_covariates are not passed to historical_forecast, None will be passed to the corresponding retrain function argument. Note: some models require being retrained every time and do not support anything other than retrain=True. Note: also controls the retraining of the data_transformers.

• overlap_end (bool) – Whether the returned forecasts can go beyond the series’ end or not.

• last_points_only (bool) – Whether to return only the last point of each historical forecast. If set to True, the method returns a single TimeSeries (for each time series in series) containing the successive point forecasts. Otherwise, returns a list of historical TimeSeries forecasts.

• verbose (bool) – Whether to print the progress.

• show_warnings (bool) – Whether to show warnings related to historical forecasts optimization, or parameters start and train_length.

• predict_likelihood_parameters (bool) – If set to True, the model predicts the parameters of its likelihood instead of the target. Only supported for probabilistic models with a likelihood, num_samples = 1 and n<=output_chunk_length. Default: False.

• enable_optimization (bool) – Whether to use the optimized version of historical_forecasts when supported and available. Default: True.

• data_transformers (Optional[dict[str, Union[BaseDataTransformer, Pipeline]], None]) –

  Optionally, a dictionary of BaseDataTransformer or Pipeline to apply to the corresponding series (possibles keys; “series”, “past_covariates”, “future_covariates”). If provided, all input series must be in the un-transformed space. For fittable transformer / pipeline:

  • if retrain=True, the data transformer re-fit on the training data at each historical forecast step.

  • if retrain=False, the data transformer transforms the series once before all the forecasts.

  The fitted transformer is used to transform the input during both training and prediction. If the transformation is invertible, the forecasts will be inverse-transformed.

• fit_kwargs (Optional[dict[str, Any], None]) – Optionally, some additional arguments passed to the model fit() method.

• predict_kwargs (Optional[dict[str, Any], None]) – Optionally, some additional arguments passed to the model predict() method.

• sample_weight (Union[TimeSeries, Sequence[TimeSeries], str, None]) – Optionally, some sample weights to apply to the target series labels for training. Only effective when retrain is not False. They are applied per observation, per label (each step in output_chunk_length), and per component. If a series or sequence of series, then those weights are used. If the weight series only have a single component / column, then the weights are applied globally to all components in series. Otherwise, for component-specific weights, the number of components must match those of series. If a string, then the weights are generated using built-in weighting functions. The available options are “linear” or “exponential” decay - the further in the past, the lower the weight. The weights are computed per time series.

Return type

Union[TimeSeries, list[TimeSeries], list[list[TimeSeries]]]

Returns

• TimeSeries – A single historical forecast for a single series and last_points_only=True: it contains only the predictions at step forecast_horizon from all historical forecasts.

• List[TimeSeries] – A list of historical forecasts for:

  • a sequence (list) of series and last_points_only=True: for each series, it contains only the predictions at step forecast_horizon from all historical forecasts.

  • a single series and last_points_only=False: for each historical forecast, it contains the entire horizon forecast_horizon.

• List[List[TimeSeries]] – A list of lists of historical forecasts for a sequence of series and last_points_only=False. For each series, and historical forecast, it contains the entire horizon forecast_horizon. The outer list is over the series provided in the input sequence, and the inner lists contain the historical forecasts for each series.

static load(path)

Loads the model from a given path or file handle.

Parameters

path (Union[str, PathLike, BinaryIO]) – Path or file handle from which to load the model.

Return type

ForecastingModel

property min_train_samples: int

The minimum number of samples for training the model.

Return type

int

property model_params: dict

Return type

dict

property output_chunk_length: Optional[int]

Number of time steps predicted at once by the model, not defined for statistical models.

Return type

Optional[int, None]

property output_chunk_shift: int

Number of time steps that the output/prediction starts after the end of the input.

Return type

int

abstract predict(n, num_samples=1, verbose=False, show_warnings=True)

Forecasts values for n time steps after the end of the training series.

Parameters

• n (int) – Forecast horizon - the number of time steps after the end of the series for which to produce predictions.

• num_samples (int) – Number of times a prediction is sampled from a probabilistic model. Must be 1 for deterministic models.

• verbose (bool) – Optionally, set the prediction verbosity. Not effective for all models.

• show_warnings (bool) – Optionally, control whether warnings are shown. Not effective for all models.

Returns

A time series containing the n next points after then end of the training series.

Return type

TimeSeries

residuals(series, past_covariates=None, future_covariates=None, historical_forecasts=None, forecast_horizon=1, num_samples=1, train_length=None, start=None, start_format='value', stride=1, retrain=True, overlap_end=False, last_points_only=True, metric=<function err>, verbose=False, show_warnings=True, predict_likelihood_parameters=False, enable_optimization=True, data_transformers=None, metric_kwargs=None, fit_kwargs=None, predict_kwargs=None, sample_weight=None, values_only=False)

Compute the residuals that the model produced for historical forecasts on (potentially multiple) series.

This function computes the difference (or one of Darts’ “per time step” metrics) between the actual observations from series and the fitted values obtained by training the model on series (or using a pre-trained model with retrain=False). Not all models support fitted values, so we use historical forecasts as an approximation for them.

In sequence this method performs:

• use pre-computed historical_forecasts or compute historical forecasts for each series (see historical_forecasts() for more details). How the historical forecasts are generated can be configured with parameters num_samples, train_length, start, start_format, forecast_horizon, stride, retrain, last_points_only, fit_kwargs, and predict_kwargs.

• compute a backtest using a “per time step” metric between the historical forecasts and series per component/column and time step (see backtest() for more details). By default, uses the residuals err() (error) as a metric.

• create and return TimeSeries (or simply a np.ndarray with values_only=True) with the time index from historical forecasts, and values from the metrics per component and time step.

This method works for single or multiple univariate or multivariate series. It uses the median prediction (when dealing with stochastic forecasts).

Parameters

• series (Union[TimeSeries, Sequence[TimeSeries]]) – A (sequence of) target time series used to successively train (if retrain is not False) and compute the historical forecasts.

• past_covariates (Union[TimeSeries, Sequence[TimeSeries], None]) – Optionally, a (sequence of) past-observed covariate time series for every input time series in series. This applies only if the model supports past covariates.

• future_covariates (Union[TimeSeries, Sequence[TimeSeries], None]) – Optionally, a (sequence of) future-known covariate time series for every input time series in series. This applies only if the model supports future covariates.

• historical_forecasts (Union[TimeSeries, Sequence[TimeSeries], Sequence[Sequence[TimeSeries]], None]) – Optionally, the (or a sequence of / a sequence of sequences of) historical forecasts time series to be evaluated. Corresponds to the output of historical_forecasts(). The same series and last_points_only values must be passed that were used to generate the historical forecasts. If provided, will skip historical forecasting and ignore all parameters except series, last_points_only, metric, and reduction.

• forecast_horizon (int) – The forecast horizon for the predictions.

• num_samples (int) – Number of times a prediction is sampled from a probabilistic model. Use values >1 only for probabilistic models.

• train_length (Optional[int, None]) – Optionally, use a fixed length / number of time steps for every constructed training set (rolling window mode). Only effective when retrain is not False. The default is None, where it uses all time steps up until the prediction time (expanding window mode). If larger than the number of available time steps, uses the expanding mode. Needs to be at least min_train_series_length.

• start (Union[Timestamp, float, int, None]) –

  Optionally, the first point in time at which a prediction is computed. This parameter supports: float, int, pandas.Timestamp, and None. If a float, it is the proportion of the time series that should lie before the first prediction point. If an int, it is either the index position of the first prediction point for series with a pd.DatetimeIndex, or the index value for series with a pd.RangeIndex. The latter can be changed to the index position with start_format=”position”. If a pandas.Timestamp, it is the time stamp of the first prediction point. If None, the first prediction point will automatically be set to:

  • the first predictable point if retrain is False, or retrain is a Callable and the first predictable point is earlier than the first trainable point.

  • the first trainable point if retrain is True or int (given train_length), or retrain is a Callable and the first trainable point is earlier than the first predictable point.

  • the first trainable point (given train_length) otherwise

  Note: If start is not within the trainable / forecastable points, uses the closest valid start point that

  is a round multiple of stride ahead of start. Raises a ValueError, if no valid start point exists.

  Note: If the model uses a shifted output (output_chunk_shift > 0), then the first predicted point is also

  shifted by output_chunk_shift points into the future.

  Note: If start is outside the possible historical forecasting times, will ignore the parameter

  (default behavior with None) and start at the first trainable/predictable point.

• start_format (Literal[‘position’, ‘value’]) – Defines the start format. If set to 'position', start corresponds to the index position of the first predicted point and can range from (-len(series), len(series) - 1). If set to 'value', start corresponds to the index value/label of the first predicted point. Will raise an error if the value is not in series’ index. Default: 'value'.

• stride (int) – The number of time steps between two consecutive predictions.

• retrain (Union[bool, int, Callable[…, bool]]) –

  Whether and/or on which condition to retrain the model before predicting. This parameter supports 3 different types: bool, (positive) int, and Callable (returning a bool). In the case of bool: retrain the model at each step (True), or never retrain the model (False). In the case of int: the model is retrained every retrain iterations. In the case of Callable: the model is retrained whenever callable returns True. The callable must have the following positional arguments:

  • counter (int): current retrain iteration

  • pred_time (pd.Timestamp or int): timestamp of forecast time (end of the training series)

  • train_series (TimeSeries): train series up to pred_time

  • past_covariates (TimeSeries): past_covariates series up to pred_time

  • future_covariates (TimeSeries): future_covariates series up to min(pred_time + series.freq * forecast_horizon, series.end_time())

  Note: if any optional *_covariates are not passed to historical_forecast, None will be passed to the corresponding retrain function argument. Note: some models require being retrained every time and do not support anything other than retrain=True. Note: also controls the retraining of the data_transformers.

• overlap_end (bool) – Whether the returned forecasts can go beyond the series’ end or not.

• last_points_only (bool) – Whether to return only the last point of each historical forecast. If set to True, the method returns a single TimeSeries (for each time series in series) containing the successive point forecasts. Otherwise, returns a list of historical TimeSeries forecasts.

• metric (Callable[…, Union[float, list[float], ndarray, list[ndarray]]]) –

  Either one of Darts’ “per time step” metrics (see here), or a custom metric that has an identical signature as Darts’ “per time step” metrics, uses decorators multi_ts_support() and multi_ts_support(), and returns one value per time step.

• verbose (bool) – Whether to print the progress.

• show_warnings (bool) – Whether to show warnings related to historical forecasts optimization, or parameters start and train_length.

• predict_likelihood_parameters (bool) – If set to True, the model predicts the parameters of its likelihood instead of the target. Only supported for probabilistic models with a likelihood, num_samples = 1 and n<=output_chunk_length. Default: False.

• enable_optimization (bool) – Whether to use the optimized version of historical_forecasts when supported and available. Default: True.

• data_transformers (Optional[dict[str, Union[BaseDataTransformer, Pipeline]], None]) –

  Optionally, a dictionary of BaseDataTransformer or Pipeline to apply to the corresponding series (possibles keys; “series”, “past_covariates”, “future_covariates”). If provided, all input series must be in the un-transformed space. For fittable transformer / pipeline:

  • if retrain=True, the data transformer re-fit on the training data at each historical forecast step.

  • if retrain=False, the data transformer transforms the series once before all the forecasts.

  The fitted transformer is used to transform the input during both training and prediction. If the transformation is invertible, the forecasts will be inverse-transformed. Only effective when historical_forecasts=None.

• metric_kwargs (Optional[dict[str, Any], None]) – Additional arguments passed to metric(), such as ‘n_jobs’ for parallelization, ‘m’ for scaled metrics, etc. Will pass arguments only if they are present in the corresponding metric signature. Ignores reduction arguments “series_reduction”, “component_reduction”, “time_reduction”, and parameter ‘insample’ for scaled metrics (e.g. mase`, rmsse, …), as they are handled internally.

• fit_kwargs (Optional[dict[str, Any], None]) – Optionally, some additional arguments passed to the model fit() method.

• predict_kwargs (Optional[dict[str, Any], None]) – Optionally, some additional arguments passed to the model predict() method.

• sample_weight (Union[TimeSeries, Sequence[TimeSeries], str, None]) – Optionally, some sample weights to apply to the target series labels for training. Only effective when retrain is not False. They are applied per observation, per label (each step in output_chunk_length), and per component. If a series or sequence of series, then those weights are used. If the weight series only have a single component / column, then the weights are applied globally to all components in series. Otherwise, for component-specific weights, the number of components must match those of series. If a string, then the weights are generated using built-in weighting functions. The available options are “linear” or “exponential” decay - the further in the past, the lower the weight. The weights are computed per time series.

• values_only (bool) – Whether to return the residuals as np.ndarray. If False, returns residuals as TimeSeries.

Return type

Union[TimeSeries, list[TimeSeries], list[list[TimeSeries]]]

Returns

• TimeSeries – Residual TimeSeries for a single series and historical_forecasts generated with last_points_only=True.

• List[TimeSeries] – A list of residual TimeSeries for a sequence (list) of series with last_points_only=True. The residual list has length len(series).

• List[List[TimeSeries]] – A list of lists of residual TimeSeries for a sequence of series with last_points_only=False. The outer residual list has length len(series). The inner lists consist of the residuals from all possible series-specific historical forecasts.

save(path=None, **pkl_kwargs)

Saves the model under a given path or file handle.

Example for saving and loading a RegressionModel:

from darts.models import RegressionModel

model = RegressionModel(lags=4)

model.save("my_model.pkl")
model_loaded = RegressionModel.load("my_model.pkl")

Parameters

• path (Union[str, PathLike, BinaryIO, None]) – Path or file handle under which to save the model at its current state. If no path is specified, the model is automatically saved under "{ModelClass}_{YYYY-mm-dd_HH_MM_SS}.pkl". E.g., "RegressionModel_2020-01-01_12_00_00.pkl".

• pkl_kwargs – Keyword arguments passed to pickle.dump()

Return type

None

property supports_future_covariates: bool

Whether model supports future covariates

Return type

bool

property supports_likelihood_parameter_prediction: bool

Whether model instance supports direct prediction of likelihood parameters

Return type

bool

abstract property supports_multivariate: bool

Whether the model considers more than one variate in the time series.

Return type

bool

property supports_optimized_historical_forecasts: bool

Whether the model supports optimized historical forecasts

Return type

bool

property supports_past_covariates: bool

Whether model supports past covariates

Return type

bool

property supports_probabilistic_prediction: bool

Checks if the forecasting model with this configuration supports probabilistic predictions.

By default, returns False. Needs to be overwritten by models that do support probabilistic predictions.

Return type

bool

property supports_sample_weight: bool

Whether model supports sample weight for training.

Return type

bool

property supports_static_covariates: bool

Whether model supports static covariates

Return type

bool

abstract property supports_transferrable_series_prediction: bool

Whether the model supports prediction for any input series.

Return type

bool

property uses_future_covariates: bool

Whether the model uses future covariates, once fitted.

Return type

bool

property uses_past_covariates: bool

Whether the model uses past covariates, once fitted.

Return type

bool

property uses_static_covariates: bool

Whether the model uses static covariates, once fitted.

Return type

bool

class darts.models.forecasting.forecasting_model.ModelMeta(name, bases, namespace, **kwargs)

Bases: ABCMeta

Meta class to store parameters used at model creation.

When creating a model instance, the parameters are extracted as follows:

1. Get the model’s __init__ signature and store all arg and kwarg names as well as default values (empty for args) in an ordered dict all_params.

2. Replace the arg values from all_params with the positional args used at model creation.

3. Remove args from all_params that were not passed as positional args at model creation. This will enforce that an error is raised if not all positional args were passed. If all positional args were passed, no parameter will be removed.

4. Update all_params kwargs with optional kwargs from model creation.

5. Save all_params to the model.

6. Call (create) the model with all_params.

Methods

__call__(*args, **kwargs)	Call self as a function.
mro(/)	Return a type's method resolution order.
register(subclass)	Register a virtual subclass of an ABC.

mro(/)

Return a type’s method resolution order.

register(subclass)

Register a virtual subclass of an ABC.

Returns the subclass, to allow usage as a class decorator.

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