ETS

class ETS(error_type: int | str = 1, trend_type: int | str | None = 0, seasonality_type: int | str | None = 0, seasonal_period: int = 1, iterations: int = 200)

Bases: BaseForecaster, IterativeForecastingMixin

Exponential Smoothing (ETS) forecaster.

Implements the ETS (Error, Trend, Seasonality) forecaster, supporting additive and multiplicative forms of error, trend (including damped), and seasonality components. Based on the state space model formulation of exponential smoothing as described in Hyndman and Athanasopoulos [1].

Parameters:

error_typestring or int, default=1

Type of error model: ‘additive’ (0) or ‘multiplicative’ (1)

trend_typestring, int or None, default=0

Type of trend component: None (0), `additive’ (1) or ‘multiplicative’ (2)

seasonality_typestring or None, default=0

Type of seasonal component: None (0), `additive’ (1) or ‘multiplicative’ (2)

seasonal_periodint, default=1

Number of time points in a seasonal cycle.

alphafloat, default=0.1

Level smoothing parameter.

betafloat, default=0.01

Trend smoothing parameter.

gammafloat, default=0.01

Seasonal smoothing parameter.

phifloat, default=0.99

Trend damping parameter (used only for damped trend models).

Attributes:

forecast_val_float

Forecast value for the given horizon.

level_float

Estimated level component.

trend_float

Estimated trend component.

seasonality_array-like or None

Estimated seasonal components.

aic_float

Akaike Information Criterion of the fitted model.

avg_mean_sq_err_float

Average mean squared error of the fitted model.

residuals_list of float

Residuals from the fitted model.

fitted_values_list of float

Fitted values for the training data.

liklihood_float

Log-likelihood of the fitted model.

n_timepoints_int

Number of time points in the training series.

Notes

Capabilities

Missing Values	No
Multithreading	No
Univariate	Yes
Multivariate	No
Horizon	No
Exogenous	No

References

[1]

R. J. Hyndman and G. Athanasopoulos, Forecasting: Principles and Practice, 2nd Edition. OTexts, 2014. https://otexts.com/fpp3/

Examples

>>> from aeon.forecasting.stats import ETS
>>> from aeon.datasets import load_airline
>>> y = load_airline()
>>> forecaster = ETS(
...     error_type='additive', trend_type='multiplicative',
...     seasonality_type='multiplicative', seasonal_period=4
... )
>>> forecaster.forecast(y)
413.0682421672687

Methods

clone([random_state])	Obtain a clone of the object with the same hyperparameters.
fit(y[, exog, axis])	Fit forecaster to series y.
forecast(y[, exog, axis])	Forecast the next horizon steps ahead of y.
get_class_tag(tag_name[, raise_error, ...])	Get tag value from estimator class (only class tags).
get_class_tags()	Get class tags from estimator class and all its parent classes.
get_fitted_params([deep])	Get fitted parameters.
get_params([deep])	Get parameters for this estimator.
get_tag(tag_name[, raise_error, ...])	Get tag value from estimator class.
get_tags()	Get tags from estimator.
iterative_forecast(y, prediction_horizon[, exog])	Forecast with ETS specific iterative method.
predict(y[, exog, axis])	Predict the next horizon steps ahead.
reset([keep])	Reset the object to a clean post-init state.
set_params(**params)	Set the parameters of this estimator.
set_tags(**tag_dict)	Set dynamic tags to given values.

clone(random_state=None)

Obtain a clone of the object with the same hyperparameters.

A clone is a different object without shared references, in post-init state. This function is equivalent to returning sklearn.clone of self. Equal in value to type(self)(**self.get_params(deep=False)).

Parameters:

random_stateint, RandomState instance, or None, default=None

Sets the random state of the clone. If None, the random state is not set. If int, random_state is the seed used by the random number generator. If RandomState instance, random_state is the random number generator.

Returns:

estimatorobject

Instance of type(self), clone of self (see above)

fit(y, exog=None, axis=1)

Fit forecaster to series y.

Fit a forecaster to predict self.horizon steps ahead using y.

Parameters:

ynp.ndarray

A time series on which to learn a forecaster to predict horizon ahead.

exognp.ndarray, default =None

Optional exogenous time series data assumed to be aligned with y.

Returns:

self

Fitted BaseForecaster.

forecast(y, exog=None, axis=1) → float

Forecast the next horizon steps ahead of y.

By default this is simply fit followed by predict.

Parameters:

ynp.ndarray

A time series to predict the next horizon value for. Must be of shape (n_channels, n_timepoints) if a multivariate time series.

exognp.ndarray, default =None

Optional exogenous time series data assumed to be aligned with y.

Returns:

float

single prediction self.horizon steps ahead of y.

classmethod get_class_tag(tag_name, raise_error=True, tag_value_default=None)

Get tag value from estimator class (only class tags).

Parameters:

tag_namestr

Name of tag value.

raise_errorbool, default=True

Whether a ValueError is raised when the tag is not found.

tag_value_defaultany type, default=None

Default/fallback value if tag is not found and error is not raised.

Returns:

tag_value

Value of the tag_name tag in cls. If not found, returns an error if raise_error is True, otherwise it returns tag_value_default.

Raises:

ValueError

if raise_error is True and tag_name is not in self.get_tags().keys()

Examples

>>> from aeon.classification import DummyClassifier
>>> DummyClassifier.get_class_tag("capability:multivariate")
True

classmethod get_class_tags()

Get class tags from estimator class and all its parent classes.

Returns:

collected_tagsdict

Dictionary of tag name and tag value pairs. Collected from _tags class attribute via nested inheritance. These are not overridden by dynamic tags set by set_tags or class __init__ calls.

get_fitted_params(deep=True)

Get fitted parameters.

State required:

Requires state to be “fitted”.

Parameters:

deepbool, default=True

If True, will return the fitted parameters for this estimator and contained subobjects that are estimators.

Returns:

fitted_paramsdict

Fitted parameter names mapped to their values.

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict

Parameter names mapped to their values.

get_tag(tag_name, raise_error=True, tag_value_default=None)

Get tag value from estimator class.

Includes dynamic and overridden tags.

Parameters:

tag_namestr

Name of tag to be retrieved.

raise_errorbool, default=True

Whether a ValueError is raised when the tag is not found.

tag_value_defaultany type, default=None

Default/fallback value if tag is not found and error is not raised.

Returns:

tag_value

Value of the tag_name tag in self. If not found, returns an error if raise_error is True, otherwise it returns tag_value_default.

Raises:

ValueError

if raise_error is True and tag_name is not in self.get_tags().keys()

Examples

>>> from aeon.classification import DummyClassifier
>>> d = DummyClassifier()
>>> d.get_tag("capability:multivariate")
True

get_tags()

Get tags from estimator.

Includes dynamic and overridden tags.

Returns:

collected_tagsdict

Dictionary of tag name and tag value pairs. Collected from _tags class attribute via nested inheritance and then any overridden and new tags from __init__ or set_tags.

iterative_forecast(y, prediction_horizon, exog=None)

Forecast with ETS specific iterative method.

Overrides the base class iterative_forecast to avoid refitting on each step. This simply rolls the ETS model forward

predict(y, exog=None, axis=1) → float

Predict the next horizon steps ahead.

Parameters:

ynp.ndarray

A time series to predict the next horizon value for.

exognp.ndarray, default =None

Optional exogenous time series data assumed to be aligned with y.

Returns:

float

single prediction self.horizon steps ahead of y.

reset(keep=None)

Reset the object to a clean post-init state.

After a self.reset() call, self is equal or similar in value to type(self)(**self.get_params(deep=False)), assuming no other attributes were kept using keep.

Detailed behaviour:

removes any object attributes, except:

hyper-parameters (arguments of __init__) object attributes containing double-underscores, i.e., the string “__”

runs __init__ with current values of hyperparameters (result of get_params)

Not affected by the reset are:

object attributes containing double-underscores class and object methods, class attributes any attributes specified in the keep argument

Parameters:

keepNone, str, or list of str, default=None

If None, all attributes are removed except hyperparameters. If str, only the attribute with this name is kept. If list of str, only the attributes with these names are kept.

Returns:

selfobject

Reference to self.

Raises:

TypeError

If ‘keep’ is not a string or a list of strings.

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.

set_tags(**tag_dict)

Set dynamic tags to given values.

Parameters:

**tag_dictdict

Dictionary of tag name and tag value pairs.

Returns:

selfobject

Reference to self.