Theta

class Theta(theta=2.0, weight=0.5)

Bases: BaseForecaster, IterativeForecastingMixin

Classical Theta forecaster.

Parameters:

thetafloat, default=2.0

Theta parameter used to form the theta line. theta=2 reproduces the classical method; values >1 accentuate curvature, <1 dampen it.

weightfloat, default=0.5

Weight assigned to the trend component in the final combination. The SES component receives (1 - weight). Values are clipped to [0, 1].

Attributes:

a_float

Estimated trend intercept from OLS on time.

b_float

Estimated trend slope from OLS on time.

alpha_float

SES smoothing parameter selected by in-sample SSE minimisation on the theta line.

forecast_float

Stored one-step-ahead forecast computed at fit time.

_tagsdict

Includes {"capability:horizon": False} to indicate closed-form multi-step forecasting (no direct multi-output training).

Notes

Capabilities

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

• The classical Theta model is equivalent to an ETS(A,N,N) with drift under certain conditions; see Hyndman & Billah (2003) for details. This implementation follows the classical two-theta construction with \(\\theta=2\) and an SES fit on the theta line.

• This is a local method: parameters are estimated per series; the model is not intended to generalise to unseen series without re-fitting.

References

[1]

Assimakopoulos, V. and Nikolopoulos, K. (2000). “The Theta model: a decomposition approach to forecasting.” International Journal of Forecasting, 16(4), 521–530.

[2]

Hyndman, R.J. and Billah, B. (2003). “Unmasking the Theta method.” International Journal of Forecasting, 19(2), 287–290.

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 prediction_horizon prediction using a single model fit on y.
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 prediction_horizon prediction using a single model fit on y.

This function implements the iterative forecasting strategy (also called recursive or iterated). This involves a single model fit on y which is then used to make prediction_horizon ahead forecasts using its own predictions as inputs for future forecasts. This is done by taking the prediction at step i and feeding it back into the model to help predict for step i+1. The basic contract of iterative_forecast is that fit is only ever called once.

ynp.ndarray

The time series to make forecasts about. Must be of shape (n_channels, n_timepoints) if a multivariate time series.

prediction_horizonint

The number of future time steps to forecast.

exognp.ndarray, default =None

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

Returns:

np.ndarray

An array of shape (prediction_horizon,) containing the forecasts for each horizon.

Raises:

ValueError

if prediction_horizon` less than 1.

Examples

>>> from aeon.forecasting import RegressionForecaster
>>> y = np.array([1.0, 2.0, 3.0, 4.0, 3.0, 2.0, 1.0, 2.0, 3.0, 4.0])
>>> f = RegressionForecaster(window=3)
>>> f.iterative_forecast(y,2)
array([3., 2.])

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.