DOTM

class DOTM(initial_level=None, alpha=None, theta=None, initial_level_bounds=(-10000000000.0, 10000000000.0), alpha_bounds=(0.1, 0.99), theta_bounds=(1.0, 10000000000.0), season_length=1, decomposition_type='multiplicative', seasonal_test='auto', max_iter=500, tol=1e-06)[source]

Bases: BaseForecaster, IterativeForecastingMixin

Dynamic Optimised Theta Model (DOTM) forecaster.

Implementation of the Dynamic Optimised Theta Model (DOTM) proposed by Fiorucci et al. (2016) [1]. DOTM is a local univariate forecaster that estimates an initial level, smoothing parameter, and theta parameter unless they are fixed by the user.

Seasonality is handled as an outer transformation: when seasonal adjustment is requested or detected, the input series is decomposed into a seasonal component and a seasonally adjusted component using classical (additive or multiplicative) decomposition with a centred moving-average trend estimate. The DOTM core is then fitted to the adjusted series, and forecasts are produced by recombining the DOTM forecast with a seasonal naive forecast of the seasonal component. The default behaviour is non-seasonal because season_length=1.

Exogenous variables and prediction intervals are not supported.

Parameters:
initial_levelfloat or None, default=None

Fixed initial level, ell0. If None, it is estimated.

alphafloat or None, default=None

Fixed smoothing parameter. If None, it is estimated.

thetafloat or None, default=None

Fixed theta parameter. If None, it is estimated.

initial_level_boundstuple of float, default=(-1e10, 1e10)

Bounds for estimated initial_level.

alpha_boundstuple of float, default=(0.1, 0.99)

Bounds for estimated alpha.

theta_boundstuple of float, default=(1.0, 1e10)

Bounds for estimated theta.

season_lengthint, default=1

Seasonal period. 1 means no seasonality.

decomposition_type{“multiplicative”, “additive”}, default=”multiplicative”

Type of classical decomposition used when the series is deseasonalised. Multiplicative decomposition falls back to additive when the input contains non-positive values or produces seasonal factors that are non-finite or smaller than 1e-8.

seasonal_test{“auto”, True, False}, default=”auto”

Controls whether to deseasonalise the series.

  • False : never deseasonalise.

  • True : deseasonalise when season_length > 1 and at least two full seasonal cycles are available.

  • "auto": apply an ACF-based seasonal test at lag season_length to the first-differenced series and deseasonalise only when seasonal evidence is present. First differencing removes a constant trend, so monotone series do not trigger spurious seasonal detection.

max_iterint, default=500

Maximum number of Nelder-Mead iterations.

tolfloat, default=1e-6

Simplex convergence tolerance.

Attributes:
initial_level_float

Fitted initial level (from the adjusted-series fit).

alpha_float

Fitted smoothing parameter.

theta_float

Fitted theta parameter.

fitted_values_np.ndarray

In-sample one-step-ahead fitted values on the original scale.

residuals_np.ndarray

In-sample residuals on the original scale (y - fitted_values_).

forecast_float

Stored one-step-ahead forecast on the original scale.

sse_float

Scaled in-sample SSE objective value from the DOTM core fit on the adjusted series.

level_float

Final level state after fitting (adjusted series).

a_float

Final dynamic line intercept state.

b_float

Final dynamic line slope state.

mean_y_float

Final running mean state.

season_length_int

Seasonal period actually used. 1 when no deseasonalisation was performed.

decomposition_type_str

Decomposition type actually used. May differ from decomposition_type if multiplicative fell back to additive.

deseasonalised_bool

Whether the input series was deseasonalised before fitting.

seasonal_factors_np.ndarray or None

Estimated seasonal factors of length season_length_, or None when deseasonalised_ is False.

Notes

Capabilities

Missing Values

No

Multithreading

No

Univariate

Yes

Multivariate

No

Horizon

No

Exogenous

No

References

[1]

Fiorucci, J. A., Pellegrini, T. R., Louzada, F., Petropoulos, F., & Koehler, A. B. (2016). Models for optimising the theta method and their relationship to state space models. International Journal of Forecasting, 32(4), 1151-1161.

Examples

>>> import numpy as np
>>> from aeon.forecasting.stats import DOTM
>>> y = np.array([2.1, 2.4, 2.8, 3.0, 3.6, 4.1])
>>> forecaster = DOTM()
>>> pred = forecaster.iterative_forecast(y, prediction_horizon=2)
>>> pred.shape
(2,)

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[, ...])

Fit DOTM on y and recursively forecast prediction_horizon steps.

predict(y[, exog, axis])

Predict the next horizon steps ahead.

reset([keep])

Reset the object to a clean post-init state.

set_fit_request(*[, axis, exog])

Configure whether metadata should be requested to be passed to the fit method.

set_params(**params)

Set the parameters of this estimator.

set_predict_request(*[, axis, exog])

Configure whether metadata should be requested to be passed to the predict method.

set_tags(**tag_dict)

Set dynamic tags to given values.
clone(random_state=None)[source]

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)[source]

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 target-time exogenous values aligned with y.

Returns:
self

Fitted BaseForecaster.

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

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 target-time exogenous values 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)[source]

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()[source]

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)[source]

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)[source]

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()[source]

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, *, future_exog=None)[source]

Fit DOTM on y and recursively forecast prediction_horizon steps.

exog and future_exog are accepted for signature compatibility with IterativeForecastingMixin but are not supported by DOTM; passing either raises NotImplementedError.

predict(y, exog=None, axis=1) → float[source]

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 values for the prediction target. For models fitted with exogenous variables, this should contain the exogenous values needed to make the next prediction.

Returns:
float

single prediction self.horizon steps ahead of y.

reset(keep=None)[source]

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_fit_request(*, axis: bool | None | str = '$UNCHANGED$', exog: bool | None | str = '$UNCHANGED$') → DOTM

Configure whether metadata should be requested to be passed to the fit method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

  • True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.

  • False: metadata is not requested and the meta-estimator will not pass it to fit.

  • None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

  • str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Parameters:
axisstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for axis parameter in fit.

exogstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for exog parameter in fit.

Returns:
selfobject

The updated object.

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_predict_request(*, axis: bool | None | str = '$UNCHANGED$', exog: bool | None | str = '$UNCHANGED$') → DOTM

Configure whether metadata should be requested to be passed to the predict method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

  • True: metadata is requested, and passed to predict if provided. The request is ignored if metadata is not provided.

  • False: metadata is not requested and the meta-estimator will not pass it to predict.

  • None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

  • str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Parameters:
axisstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for axis parameter in predict.

exogstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for exog parameter in predict.

Returns:
selfobject

The updated object.

set_tags(**tag_dict)[source]

Set dynamic tags to given values.

Parameters:
**tag_dictdict

Dictionary of tag name and tag value pairs.

Returns:
selfobject

Reference to self.