# UnobservedComponents#

class UnobservedComponents(level=False, trend=False, seasonal=None, freq_seasonal=None, cycle=False, autoregressive=None, irregular=False, stochastic_level=False, stochastic_trend=False, stochastic_seasonal=True, stochastic_freq_seasonal=None, stochastic_cycle=False, damped_cycle=False, cycle_period_bounds=None, mle_regression=True, use_exact_diffuse=False, start_params=None, transformed=True, includes_fixed=False, cov_type=None, cov_kwds=None, method='lbfgs', maxiter=50, full_output=1, disp=0, callback=None, return_params=False, optim_score=None, optim_complex_step=None, optim_hessian=None, flags=None, low_memory=False, random_state=None)[source]#

Wrapper class of the UnobservedComponents model from statsmodels.

Input parameters and doc-stringsare taken from the original implementation.

Parameters
level{bool, str}, optional

Whether or not to include a level component. Default is False. Can also be a string specification of the level / trend component.

trendbool, optional

Whether or not to include a trend component. Default is False. If True, level must also be True.

seasonal{int, None}, optional

The period of the seasonal component, if any. Default is None.

freq_seasonal{list[dict], None}, optional.

Whether (and how) to model seasonal component(s) with trig. functions. If specified, there is one dictionary for each frequency-domain seasonal component. Each dictionary must have the key, value pair for ‘period’ – integer and may have a key, value pair for ‘harmonics’ – integer. If ‘harmonics’ is not specified in any of the dictionaries, it defaults to the floor of period/2.

cyclebool, optional

Whether or not to include a cycle component. Default is False.

autoregressive{int, None}, optional

The order of the autoregressive component. Default is None.

irregularbool, optional

Whether or not to include an irregular component. Default is False.

stochastic_levelbool, optional

Whether or not any level component is stochastic. Default is False.

stochastic_trendbool, optional

Whether or not any trend component is stochastic. Default is False.

stochastic_seasonalbool, optional

Whether or not any seasonal component is stochastic. Default is True.

stochastic_freq_seasonallist[bool], optional

Whether or not each seasonal component(s) is (are) stochastic. Default is True for each component. The list should be of the same length as freq_seasonal.

stochastic_cyclebool, optional

Whether or not any cycle component is stochastic. Default is False.

damped_cyclebool, optional

Whether or not the cycle component is damped. Default is False.

cycle_period_boundstuple, optional

A tuple with lower and upper allowed bounds for the period of the cycle. If not provided, the following default bounds are used: (1) if no date / time information is provided, the frequency is constrained to be between zero and $$\pi$$, so the period is constrained to be in [0.5, infinity]. (2) If the date / time information is provided, the default bounds allow the cyclical component to be between 1.5 and 12 years; depending on the frequency of the endogenous variable, this will imply different specific bounds.

mle_regressionbool, optional

Whether or not to estimate regression coefficients by maximum likelihood as one of hyperparameters. Default is True. If False, the regression coefficients are estimated by recursive OLS, included in the state vector.

use_exact_diffusebool, optional

Whether or not to use exact diffuse initialization for non-stationary states. Default is False (in which case approximate diffuse initialization is used).

start_paramsarray_like, optional

Initial guess of the solution for the loglikelihood maximization.

transformedbool, optional

Whether or not start_params is already transformed. Default is True.

includes_fixedbool, optional

If parameters were previously fixed with the fix_params method, this argument describes whether or not start_params also includes the fixed parameters, in addition to the free parameters. Default is False.

cov_typestr, optional

The cov_type keyword governs the method for calculating the covariance matrix of parameter estimates. Can be one of: - ‘opg’ for the outer product of gradient estimator - ‘oim’ for the observed information matrix estimator, calculated

using the method of Harvey (1989)

• ‘approx’ for the observed information matrix estimator,

calculated using a numerical approximation of the Hessian matrix.

• ‘robust’ for an approximate (quasi-maximum likelihood) covariance

matrix that may be valid even in the presence of some misspecifications. Intermediate calculations use the ‘oim’ method.

• ‘robust_approx’ is the same as ‘robust’ except that the

intermediate calculations use the ‘approx’ method.

• ‘none’ for no covariance matrix calculation.

Default is ‘opg’ unless memory conservation is used to avoid computing the loglikelihood values for each observation, in which case the default is ‘approx’.

cov_kwdsdict or None, optional

A dictionary of arguments affecting covariance matrix computation. opg, oim, approx, robust, robust_approx - ‘approx_complex_step’ : bool, optional - If True, numerical

approximations are computed using complex-step methods. If False, numerical approximations are computed using finite difference methods. Default is True.

• ‘approx_centered’bool, optional - If True, numerical

approximations computed using finite difference methods use a centered approximation. Default is False.

methodstr, optional

The method determines which solver from scipy.optimize is used, and it can be chosen from among the following strings: - ‘newton’ for Newton-Raphson - ‘nm’ for Nelder-Mead - ‘bfgs’ for Broyden-Fletcher-Goldfarb-Shanno (BFGS) - ‘lbfgs’ for limited-memory BFGS with optional box constraints - ‘powell’ for modified Powell’s method - ‘cg’ for conjugate gradient - ‘ncg’ for Newton-conjugate gradient - ‘basinhopping’ for global basin-hopping solver The explicit arguments in fit are passed to the solver, with the exception of the basin-hopping solver. Each solver has several optional arguments that are not the same across solvers. See the notes section below (or scipy.optimize) for the available arguments and for the list of explicit arguments that the basin-hopping solver supports.

maxiterint, optional

The maximum number of iterations to perform.

full_outputbool, optional

Set to True to have all available output in the Results object’s mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information.

dispbool, optional

Set to True to print convergence messages. Default is 0.

callbackcallable callback(xk), optional

Called after each iteration, as callback(xk), where xk is the current parameter vector.

return_paramsbool, optional

Whether or not to return only the array of maximizing parameters. Default is False.

optim_score{‘harvey’, ‘approx’} or None, optional

The method by which the score vector is calculated. ‘harvey’ uses the method from Harvey (1989), ‘approx’ uses either finite difference or complex step differentiation depending upon the value of optim_complex_step, and None uses the built-in gradient approximation of the optimizer. Default is None. This keyword is only relevant if the optimization method uses the score.

optim_complex_stepbool, optional

Whether or not to use complex step differentiation when approximating the score; if False, finite difference approximation is used. Default is True. This keyword is only relevant if optim_score is set to ‘harvey’ or ‘approx’.

optim_hessian{‘opg’,’oim’,’approx’}, optional

The method by which the Hessian is numerically approximated. ‘opg’ uses outer product of gradients, ‘oim’ uses the information matrix formula from Harvey (1989), and ‘approx’ uses numerical approximation. This keyword is only relevant if the optimization method uses the Hessian matrix.

low_memorybool, optional

If set to True, techniques are applied to substantially reduce memory usage. If used, some features of the results object will not be available (including smoothed results and in-sample prediction), although out-of-sample forecasting is possible. Default is False.

random_stateint, RandomState instance or None, optional ,

default=None – If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Attributes
cutoff

Cut-off = “present time” state of forecaster.

fh

Forecasting horizon that was passed.

is_fitted

Whether fit has been called.

References

1

Seabold, Skipper, and Josef Perktold. “statsmodels: Econometric and statistical modeling with python.” Proceedings of the 9th Python in Science Conference. 2010.

2

Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods: Second Edition. Oxford University Press.

Examples

>>> from sktime.datasets import load_airline
>>> from sktime.forecasting.structural import UnobservedComponents
>>> forecaster = UnobservedComponents(level='local linear trend')
>>> forecaster.fit(y)
UnobservedComponents(...)
>>> y_pred = forecaster.predict(fh=[1, 2, 3])


Methods

 Check if the estimator has been fitted. Obtain a clone of the object with same hyper-parameters. clone_tags(estimator[, tag_names]) clone/mirror tags from another estimator as dynamic override. create_test_instance([parameter_set]) Construct Estimator instance if possible. create_test_instances_and_names([parameter_set]) Create list of all test instances and a list of names for them. fit(y[, X, fh]) Fit forecaster to training data. fit_predict(y[, X, fh]) Fit and forecast time series at future horizon. get_class_tag(tag_name[, tag_value_default]) Get tag value from estimator class (only class tags). Get class tags from estimator class and all its parent classes. get_fitted_params([deep]) Get fitted parameters. Get parameter defaults for the object. Get parameter names for the object. get_params([deep]) Get parameters for this estimator. get_tag(tag_name[, tag_value_default, …]) Get tag value from estimator class and dynamic tag overrides. Get tags from estimator class and dynamic tag overrides. get_test_params([parameter_set]) Return testing parameter settings for the estimator. Check if the object is composite. load_from_path(serial) Load object from file location. load_from_serial(serial) Load object from serialized memory container. plot_diagnostics([variable, lags, fig, …]) Diagnostic plots for standardized residuals. predict([fh, X]) Forecast time series at future horizon. predict_interval([fh, X, coverage]) Compute/return prediction interval forecasts. predict_proba([fh, X, marginal]) Compute/return fully probabilistic forecasts. predict_quantiles([fh, X, alpha]) Compute/return quantile forecasts. predict_residuals([y, X]) Return residuals of time series forecasts. predict_var([fh, X, cov]) Compute/return variance forecasts. Reset the object to a clean post-init state. save([path]) Save serialized self to bytes-like object or to (.zip) file. score(y[, X, fh]) Scores forecast against ground truth, using MAPE. set_params(**params) Set the parameters of this object. set_tags(**tag_dict) Set dynamic tags to given values. simulate(nsimulations[, X, …]) Simulate a new time series following the state space model. Get a summary of the fitted forecaster. update(y[, X, update_params]) Update cutoff value and, optionally, fitted parameters. update_predict(y[, cv, X, update_params, …]) Make predictions and update model iteratively over the test set. update_predict_single([y, fh, X, update_params]) Update model with new data and make forecasts.
summary()[source]#

Get a summary of the fitted forecaster.

This is the same as the implementation in statsmodels: https://www.statsmodels.org/dev/examples/notebooks/generated/statespace_structural_harvey_jaeger.html

simulate(nsimulations, X=None, measurement_shocks=None, state_shocks=None, initial_state=None, anchor=None, repetitions=None, **kwargs)[source]#

Simulate a new time series following the state space model.

Taken from the original statsmodels implementation.

Parameters
nsimulationsint

The number of observations to simulate. If the model is time-invariant this can be any number. If the model is time-varying, then this number must be less than or equal to the number of observations.

Xpd.DataFrame, optional (default=None)

Exogenous variables.

measurement_shocksarray_like, optional

If specified, these are the shocks to the measurement equation, $$\varepsilon_t$$. If unspecified, these are automatically generated using a pseudo-random number generator. If specified, must be shaped nsimulations x k_endog, where k_endog is the same as in the state space model.

state_shocksarray_like, optional

If specified, these are the shocks to the state equation, $$\eta_t$$. If unspecified, these are automatically generated using a pseudo-random number generator. If specified, must be shaped nsimulations x k_posdef where k_posdef is the same as in the state space model.

initial_statearray_like, optional

If specified, this is the initial state vector to use in simulation, which should be shaped (k_states x 1), where k_states is the same as in the state space model. If unspecified, but the model has been initialized, then that initialization is used. This must be specified if anchor is anything other than “start” or 0 (or else you can use the simulate method on a results object rather than on the model object).

anchorint, str, or datetime, optional

First period for simulation. The simulation will be conditional on all existing datapoints prior to the anchor. Type depends on the index of the given endog in the model. Two special cases are the strings ‘start’ and ‘end’. start refers to beginning the simulation at the first period of the sample, and end refers to beginning the simulation at the first period after the sample. Integer values can run from 0 to nobs, or can be negative to apply negative indexing. Finally, if a date/time index was provided to the model, then this argument can be a date string to parse or a datetime type. Default is ‘start’.

repetitionsint, optional

Number of simulated paths to generate. Default is 1 simulated path.

Returns
simulated_obsndarray

An array of simulated observations. If repetitions=None, then it will be shaped (nsimulations x k_endog) or (nsimulations,) if k_endog=1. Otherwise it will be shaped (nsimulations x k_endog x repetitions). If the model was given Pandas input then the output will be a Pandas object. If k_endog > 1 and repetitions is not None, then the output will be a Pandas DataFrame that has a MultiIndex for the columns, with the first level containing the names of the endog variables and the second level containing the repetition number.

plot_diagnostics(variable=0, lags=10, fig=None, figsize=None, truncate_endog_names=24)[source]#

Diagnostic plots for standardized residuals.

Taken from the original statsmodels implementation.

Parameters
variableint, optional

Index of the endogenous variable for which the diagnostic plots should be created. Default is 0.

lagsint, optional

Number of lags to include in the correlogram. Default is 10.

figFigure, optional

If given, subplots are created in this figure instead of in a new figure. Note that the 2x2 grid will be created in the provided figure using fig.add_subplot().

figsizetuple, optional

If a figure is created, this argument allows specifying a size. The tuple is (width, height).

Returns
Figure

Figure instance with diagnostic plots.

classmethod get_test_params(parameter_set='default')[source]#

Return testing parameter settings for the estimator.

Parameters
parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns
paramsdict or list of dict, default = {}

Parameters to create testing instances of the class Each dict are parameters to construct an “interesting” test instance, i.e., MyClass(**params) or MyClass(**params[i]) creates a valid test instance. create_test_instance uses the first (or only) dictionary in params

check_is_fitted()[source]#

Check if the estimator has been fitted.

Raises
NotFittedError

If the estimator has not been fitted yet.

clone()[source]#

Obtain a clone of the object with same hyper-parameters.

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)).

Returns
instance of type(self), clone of self (see above)
clone_tags(estimator, tag_names=None)[source]#

clone/mirror tags from another estimator as dynamic override.

Parameters
estimatorestimator inheriting from :class:BaseEstimator
tag_namesstr or list of str, default = None

Names of tags to clone. If None then all tags in estimator are used as tag_names.

Returns
Self

Reference to self.

Notes

Changes object state by setting tag values in tag_set from estimator as dynamic tags in self.

classmethod create_test_instance(parameter_set='default')[source]#

Construct Estimator instance if possible.

Parameters
parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns
instanceinstance of the class with default parameters

Notes

get_test_params can return dict or list of dict. This function takes first or single dict that get_test_params returns, and constructs the object with that.

classmethod create_test_instances_and_names(parameter_set='default')[source]#

Create list of all test instances and a list of names for them.

Parameters
parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns
objslist of instances of cls

i-th instance is cls(**cls.get_test_params()[i])

nameslist of str, same length as objs

i-th element is name of i-th instance of obj in tests convention is {cls.__name__}-{i} if more than one instance otherwise {cls.__name__}

parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

property cutoff[source]#

Cut-off = “present time” state of forecaster.

Returns
cutoffpandas compatible index element, or None

pandas compatible index element, if cutoff has been set; None otherwise

property fh[source]#

Forecasting horizon that was passed.

fit(y, X=None, fh=None)[source]#

Fit forecaster to training data.

State change:

Changes state to “fitted”.

Writes to self:

Sets self._is_fitted flag to True. Writes self._y and self._X with y and X, respectively. Sets self.cutoff and self._cutoff to last index seen in y. Sets fitted model attributes ending in “_”. Stores fh to self.fh if fh is passed.

Parameters
ytime series in sktime compatible data container format

Time series to which to fit the forecaster.

y can be in one of the following formats: Series scitype: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D)

for vanilla forecasting, one time series

Panel scitype: pd.DataFrame with 2-level row MultiIndex,

3D np.ndarray, list of Series pd.DataFrame, or nested pd.DataFrame for global or panel forecasting

Hierarchical scitype: pd.DataFrame with 3 or more level row MultiIndex

for hierarchical forecasting

Number of columns admissible depend on the “scitype:y” tag:
if self.get_tag(“scitype:y”)==”univariate”:

y must have a single column/variable

if self.get_tag(“scitype:y”)==”multivariate”:

y must have 2 or more columns

if self.get_tag(“scitype:y”)==”both”: no restrictions on columns apply

For further details:

on usage, see forecasting tutorial examples/01_forecasting.ipynb on specification of formats, examples/AA_datatypes_and_datasets.ipynb

fhint, list, np.array or ForecastingHorizon, optional (default=None)

The forecasting horizon encoding the time stamps to forecast at. if self.get_tag(“requires-fh-in-fit”), must be passed, not optional

Xtime series in sktime compatible format, optional (default=None)

Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y if self.get_tag(“X-y-must-have-same-index”), X.index must contain y.index there are no restrictions on number of columns (unlike for y)

Returns
selfReference to self.
fit_predict(y, X=None, fh=None)[source]#

Fit and forecast time series at future horizon.

State change:

Changes state to “fitted”.

Writes to self:

Sets is_fitted flag to True. Writes self._y and self._X with y and X, respectively. Sets self.cutoff and self._cutoff to last index seen in y. Sets fitted model attributes ending in “_”. Stores fh to self.fh.

Parameters
ytime series in sktime compatible data container format

Time series to which to fit the forecaster.

y can be in one of the following formats: Series scitype: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D)

for vanilla forecasting, one time series

Panel scitype: pd.DataFrame with 2-level row MultiIndex,

3D np.ndarray, list of Series pd.DataFrame, or nested pd.DataFrame for global or panel forecasting

Hierarchical scitype: pd.DataFrame with 3 or more level row MultiIndex

for hierarchical forecasting

Number of columns admissible depend on the “scitype:y” tag:
if self.get_tag(“scitype:y”)==”univariate”:

y must have a single column/variable

if self.get_tag(“scitype:y”)==”multivariate”:

y must have 2 or more columns

if self.get_tag(“scitype:y”)==”both”: no restrictions on columns apply

For further details:

on usage, see forecasting tutorial examples/01_forecasting.ipynb on specification of formats, examples/AA_datatypes_and_datasets.ipynb

fhint, list, np.array or ForecastingHorizon (not optional)

The forecasting horizon encoding the time stamps to forecast at. if has not been passed in fit, must be passed, not optional

Xtime series in sktime compatible format, optional (default=None)

Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y in fit if self.get_tag(“X-y-must-have-same-index”),

X.index must contain fh.index and y.index both

Returns
y_predtime series in sktime compatible data container format

Point forecasts at fh, with same index as fh y_pred has same type as the y that has been passed most recently:

Series, Panel, Hierarchical scitype, same format (see above)

classmethod get_class_tag(tag_name, tag_value_default=None)[source]#

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

Parameters
tag_namestr

Name of tag value.

tag_value_defaultany type

Returns
tag_value

Value of the tag_name tag in self. If not found, returns tag_value_default.

classmethod get_class_tags()[source]#

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

Returns
collected_tagsdict

Dictionary of tag name : tag value pairs. Collected from _tags class attribute via nested inheritance. NOT overridden by dynamic tags set by set_tags or mirror_tags.

get_fitted_params(deep=True)[source]#

Get fitted parameters.

State required:

Requires state to be “fitted”.

Parameters
deepbool, default=True

Whether to return fitted parameters of components.

• If True, will return a dict of parameter name : value for this object, including fitted parameters of fittable components (= BaseEstimator-valued parameters).

• If False, will return a dict of parameter name : value for this object, but not include fitted parameters of components.

Returns
fitted_paramsdict with str-valued keys

Dictionary of fitted parameters, paramname : paramvalue keys-value pairs include:

• always: all fitted parameters of this object, as via get_param_names values are fitted parameter value for that key, of this object

• if deep=True, also contains keys/value pairs of component parameters parameters of components are indexed as [componentname]__[paramname] all parameters of componentname appear as paramname with its value

• if deep=True, also contains arbitrary levels of component recursion, e.g., [componentname]__[componentcomponentname]__[paramname], etc

classmethod get_param_defaults()[source]#

Get parameter defaults for the object.

Returns
default_dict: dict with str keys

keys are all parameters of cls that have a default defined in __init__ values are the defaults, as defined in __init__

classmethod get_param_names()[source]#

Get parameter names for the object.

Returns
param_names: list of str, alphabetically sorted list of parameter names of cls
get_params(deep=True)[source]#

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, tag_value_default=None, raise_error=True)[source]#

Get tag value from estimator class and dynamic tag overrides.

Parameters
tag_namestr

Name of tag to be retrieved

tag_value_defaultany type, optional; default=None

raise_errorbool

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 i.e. if tag_name is not in self.get_tags(
).keys()
get_tags()[source]#

Get tags from estimator class and dynamic tag overrides.

Returns
collected_tagsdict

Dictionary of tag name : tag value pairs. Collected from _tags class attribute via nested inheritance and then any overrides and new tags from _tags_dynamic object attribute.

is_composite()[source]#

Check if the object is composite.

A composite object is an object which contains objects, as parameters. Called on an instance, since this may differ by instance.

Returns
composite: bool, whether self contains a parameter which is BaseObject
property is_fitted[source]#

Whether fit has been called.

Parameters
serialresult of ZipFile(path).open(“object)
Returns
deserialized self resulting in output at path, of cls.save(path)

Load object from serialized memory container.

Parameters
serial1st element of output of cls.save(None)
Returns
deserialized self resulting in output serial, of cls.save(None)
predict(fh=None, X=None)[source]#

Forecast time series at future horizon.

State required:

Requires state to be “fitted”.

Accesses in self:

Fitted model attributes ending in “_”. self.cutoff, self._is_fitted

Writes to self:

Stores fh to self.fh if fh is passed and has not been passed previously.

Parameters
fhint, list, np.array or ForecastingHorizon, optional (default=None)

The forecasting horizon encoding the time stamps to forecast at. if has not been passed in fit, must be passed, not optional

Xtime series in sktime compatible format, optional (default=None)

Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y in fit if self.get_tag(“X-y-must-have-same-index”), X.index must contain fh.index there are no restrictions on number of columns (unlike for y)

Returns
y_predtime series in sktime compatible data container format

Point forecasts at fh, with same index as fh y_pred has same type as the y that has been passed most recently:

Series, Panel, Hierarchical scitype, same format (see above)

predict_interval(fh=None, X=None, coverage=0.9)[source]#

Compute/return prediction interval forecasts.

If coverage is iterable, multiple intervals will be calculated.

State required:

Requires state to be “fitted”.

Accesses in self:

Fitted model attributes ending in “_”. self.cutoff, self._is_fitted

Writes to self:

Stores fh to self.fh if fh is passed and has not been passed previously.

Parameters
fhint, list, np.array or ForecastingHorizon (not optional)

The forecasting horizon encoding the time stamps to forecast at. if has not been passed in fit, must be passed, not optional

Xtime series in sktime compatible format, optional (default=None)

Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y in fit if self.get_tag(“X-y-must-have-same-index”), must contain fh.index

coveragefloat or list of float of unique values, optional (default=0.90)

nominal coverage(s) of predictive interval(s)

Returns
pred_intpd.DataFrame
Column has multi-index: first level is variable name from y in fit,
second level coverage fractions for which intervals were computed.

in the same order as in input coverage.

Third level is string “lower” or “upper”, for lower/upper interval end.

Row index is fh, with additional (upper) levels equal to instance levels,

from y seen in fit, if y seen in fit was Panel or Hierarchical.

Entries are forecasts of lower/upper interval end,

for var in col index, at nominal coverage in second col index, lower/upper depending on third col index, for the row index. Upper/lower interval end forecasts are equivalent to quantile forecasts at alpha = 0.5 - c/2, 0.5 + c/2 for c in coverage.

predict_proba(fh=None, X=None, marginal=True)[source]#

Compute/return fully probabilistic forecasts.

Note: currently only implemented for Series (non-panel, non-hierarchical) y.

State required:

Requires state to be “fitted”.

Accesses in self:

Fitted model attributes ending in “_”. self.cutoff, self._is_fitted

Writes to self:

Stores fh to self.fh if fh is passed and has not been passed previously.

Parameters
fhint, list, np.array or ForecastingHorizon (not optional)

The forecasting horizon encoding the time stamps to forecast at. if has not been passed in fit, must be passed, not optional

Xtime series in sktime compatible format, optional (default=None)

Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y in fit if self.get_tag(“X-y-must-have-same-index”), must contain fh.index

marginalbool, optional (default=True)

whether returned distribution is marginal by time index

Returns
pred_disttfp Distribution object
if marginal=True:

batch shape is 1D and same length as fh event shape is 1D, with length equal number of variables being forecast i-th (batch) distribution is forecast for i-th entry of fh j-th (event) index is j-th variable, order as y in fit/update

if marginal=False:

there is a single batch event shape is 2D, of shape (len(fh), no. variables) i-th (event dim 1) distribution is forecast for i-th entry of fh j-th (event dim 1) index is j-th variable, order as y in fit/update

predict_quantiles(fh=None, X=None, alpha=None)[source]#

Compute/return quantile forecasts.

If alpha is iterable, multiple quantiles will be calculated.

State required:

Requires state to be “fitted”.

Accesses in self:

Fitted model attributes ending in “_”. self.cutoff, self._is_fitted

Writes to self:

Stores fh to self.fh if fh is passed and has not been passed previously.

Parameters
fhint, list, np.array or ForecastingHorizon (not optional)

The forecasting horizon encoding the time stamps to forecast at. if has not been passed in fit, must be passed, not optional

Xtime series in sktime compatible format, optional (default=None)

Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y in fit if self.get_tag(“X-y-must-have-same-index”), must contain fh.index

alphafloat or list of float of unique values, optional (default=[0.05, 0.95])

A probability or list of, at which quantile forecasts are computed.

Returns
quantilespd.DataFrame
Column has multi-index: first level is variable name from y in fit,

second level being the values of alpha passed to the function.

Row index is fh, with additional (upper) levels equal to instance levels,

from y seen in fit, if y seen in fit was Panel or Hierarchical.

Entries are quantile forecasts, for var in col index,

at quantile probability in second col index, for the row index.

predict_residuals(y=None, X=None)[source]#

Return residuals of time series forecasts.

Residuals will be computed for forecasts at y.index.

If fh must be passed in fit, must agree with y.index. If y is an np.ndarray, and no fh has been passed in fit, the residuals will be computed at a fh of range(len(y.shape[0]))

State required:

Requires state to be “fitted”. If fh has been set, must correspond to index of y (pandas or integer)

Accesses in self:

Fitted model attributes ending in “_”. self.cutoff, self._is_fitted

Writes to self:

Nothing.

Parameters
ytime series in sktime compatible data container format

Time series with ground truth observations, to compute residuals to. Must have same type, dimension, and indices as expected return of predict. if None, the y seen so far (self._y) are used, in particular:

if preceded by a single fit call, then in-sample residuals are produced if fit requires fh, it must have pointed to index of y in fit

Xpd.DataFrame, or 2D np.ndarray, optional (default=None)

Exogeneous time series to predict from if self.get_tag(“X-y-must-have-same-index”),

X.index must contain fh.index and y.index both

Returns
y_restime series in sktime compatible data container format

Forecast residuals at fh, with same index as fh y_res has same type as the y that has been passed most recently:

Series, Panel, Hierarchical scitype, same format (see above)

predict_var(fh=None, X=None, cov=False)[source]#

Compute/return variance forecasts.

State required:

Requires state to be “fitted”.

Accesses in self:

Fitted model attributes ending in “_”. self.cutoff, self._is_fitted

Writes to self:

Stores fh to self.fh if fh is passed and has not been passed previously.

Parameters
fhint, list, np.array or ForecastingHorizon (not optional)

The forecasting horizon encoding the time stamps to forecast at. if has not been passed in fit, must be passed, not optional

Xtime series in sktime compatible format, optional (default=None)

Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y in fit if self.get_tag(“X-y-must-have-same-index”),

X.index must contain fh.index and y.index both

covbool, optional (default=False)

if True, computes covariance matrix forecast. if False, computes marginal variance forecasts.

Returns
pred_varpd.DataFrame, format dependent on cov variable
If cov=False:
Column names are exactly those of y passed in fit/update.

For nameless formats, column index will be a RangeIndex.

Row index is fh, with additional levels equal to instance levels,

from y seen in fit, if y seen in fit was Panel or Hierarchical.

Entries are variance forecasts, for var in col index. A variance forecast for given variable and fh index is a predicted

variance for that variable and index, given observed data.

If cov=True:
Column index is a multiindex: 1st level is variable names (as above)

2nd level is fh.

Row index is fh, with additional levels equal to instance levels,

from y seen in fit, if y seen in fit was Panel or Hierarchical.

Entries are (co-)variance forecasts, for var in col index, and

covariance between time index in row and col.

Note: no covariance forecasts are returned between different variables.

reset()[source]#

Reset the object to a clean post-init state.

Equivalent to sklearn.clone but overwrites self. After self.reset() call, self is equal in value to type(self)(**self.get_params(deep=False))

Detail 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 hyper-parameters (result of get_params)

Not affected by the reset are: object attributes containing double-underscores class and object methods, class attributes

save(path=None)[source]#

Save serialized self to bytes-like object or to (.zip) file.

Behaviour: if path is None, returns an in-memory serialized self if path is a file location, stores self at that location as a zip file

saved files are zip files with following contents: _metadata - contains class of self, i.e., type(self) _obj - serialized self. This class uses the default serialization (pickle).

Parameters
pathNone or file location (str or Path)

if None, self is saved to an in-memory object if file location, self is saved to that file location. If:

path=”estimator” then a zip file estimator.zip will be made at cwd. path=”/home/stored/estimator” then a zip file estimator.zip will be stored in /home/stored/.

Returns
if path is None - in-memory serialized self
if path is file location - ZipFile with reference to the file
score(y, X=None, fh=None)[source]#

Scores forecast against ground truth, using MAPE.

Parameters
ypd.Series, pd.DataFrame, or np.ndarray (1D or 2D)

Time series to score if self.get_tag(“scitype:y”)==”univariate”:

must have a single column/variable

if self.get_tag(“scitype:y”)==”multivariate”:

must have 2 or more columns

if self.get_tag(“scitype:y”)==”both”: no restrictions apply

fhint, list, array-like or ForecastingHorizon, optional (default=None)

The forecasters horizon with the steps ahead to to predict.

Xpd.DataFrame, or 2D np.array, optional (default=None)

Exogeneous time series to score if self.get_tag(“X-y-must-have-same-index”), X.index must contain y.index

Returns
scorefloat

sMAPE loss of self.predict(fh, X) with respect to y_test.

set_params(**params)[source]#

Set the parameters of this object.

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

Parameters
**paramsdict

BaseObject parameters

Returns
selfreference to self (after parameters have been set)
set_tags(**tag_dict)[source]#

Set dynamic tags to given values.

Parameters
tag_dictdict

Dictionary of tag name : tag value pairs.

Returns
Self

Reference to self.

Notes

Changes object state by settting tag values in tag_dict as dynamic tags in self.

update(y, X=None, update_params=True)[source]#

Update cutoff value and, optionally, fitted parameters.

If no estimator-specific update method has been implemented, default fall-back is as follows:

update_params=True: fitting to all observed data so far update_params=False: updates cutoff and remembers data only

State required:

Requires state to be “fitted”.

Accesses in self:

Fitted model attributes ending in “_”. Pointers to seen data, self._y and self.X self.cutoff, self._is_fitted If update_params=True, model attributes ending in “_”.

Writes to self:

Update self._y and self._X with y and X, by appending rows. Updates self.cutoff and self._cutoff to last index seen in y. If update_params=True,

updates fitted model attributes ending in “_”.

Parameters
ytime series in sktime compatible data container format

Time series to which to fit the forecaster in the update.

y can be in one of the following formats, must be same scitype as in fit: Series scitype: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D)

for vanilla forecasting, one time series

Panel scitype: pd.DataFrame with 2-level row MultiIndex,

3D np.ndarray, list of Series pd.DataFrame, or nested pd.DataFrame for global or panel forecasting

Hierarchical scitype: pd.DataFrame with 3 or more level row MultiIndex

for hierarchical forecasting

Number of columns admissible depend on the “scitype:y” tag:
if self.get_tag(“scitype:y”)==”univariate”:

y must have a single column/variable

if self.get_tag(“scitype:y”)==”multivariate”:

y must have 2 or more columns

if self.get_tag(“scitype:y”)==”both”: no restrictions on columns apply

For further details:

on usage, see forecasting tutorial examples/01_forecasting.ipynb on specification of formats, examples/AA_datatypes_and_datasets.ipynb

Xtime series in sktime compatible format, optional (default=None)

Exogeneous time series to fit to

Should be of same scitype (Series, Panel, or Hierarchical) as y if self.get_tag(“X-y-must-have-same-index”), X.index must contain y.index there are no restrictions on number of columns (unlike for y)

update_paramsbool, optional (default=True)

whether model parameters should be updated

Returns
selfreference to self
update_predict(y, cv=None, X=None, update_params=True, reset_forecaster=True)[source]#

Make predictions and update model iteratively over the test set.

State required:

Requires state to be “fitted”.

Accesses in self:

Fitted model attributes ending in “_”. Pointers to seen data, self._y and self.X self.cutoff, self._is_fitted If update_params=True, model attributes ending in “_”.

Writes to self, if reset_forecaster=False:

Update self._y and self._X with y and X, by appending rows. Updates self.cutoff and self._cutoff to last index seen in y. If update_params=True,

updates fitted model attributes ending in “_”.

Does not update state if reset_forecaster=True.

Parameters
ytime series in sktime compatible data container format

Time series to which to fit the forecaster in the update.

y can be in one of the following formats, must be same scitype as in fit: Series scitype: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D)

for vanilla forecasting, one time series

Panel scitype: pd.DataFrame with 2-level row MultiIndex,

3D np.ndarray, list of Series pd.DataFrame, or nested pd.DataFrame for global or panel forecasting

Hierarchical scitype: pd.DataFrame with 3 or more level row MultiIndex

for hierarchical forecasting

Number of columns admissible depend on the “scitype:y” tag:
if self.get_tag(“scitype:y”)==”univariate”:

y must have a single column/variable

if self.get_tag(“scitype:y”)==”multivariate”:

y must have 2 or more columns

if self.get_tag(“scitype:y”)==”both”: no restrictions on columns apply

For further details:

on usage, see forecasting tutorial examples/01_forecasting.ipynb on specification of formats, examples/AA_datatypes_and_datasets.ipynb

cvtemporal cross-validation generator inheriting from BaseSplitter, optional

for example, SlidingWindowSplitter or ExpandingWindowSplitter default = ExpandingWindowSplitter with initial_window=1 and defaults

= individual data points in y/X are added and forecast one-by-one, initial_window = 1, step_length = 1 and fh = 1

Xtime series in sktime compatible format, optional (default=None)

Exogeneous time series for updating and forecasting Should be of same scitype (Series, Panel, or Hierarchical) as y if self.get_tag(“X-y-must-have-same-index”),

X.index must contain y.index and fh.index both

there are no restrictions on number of columns (unlike for y)

update_paramsbool, optional (default=True)

whether model parameters should be updated in each update step

reset_forecasterbool, optional (default=True)
if True, will not change the state of the forecaster,

i.e., update/predict sequence is run with a copy, and cutoff, model parameters, data memory of self do not change

if False, will update self when the update/predict sequence is run

as if update/predict were called directly

Returns
y_predobject that tabulates point forecasts from multiple split batches

format depends on pairs (cutoff, absolute horizon) forecast overall if collection of absolute horizon points is unique:

type is time series in sktime compatible data container format cutoff is suppressed in output has same type as the y that has been passed most recently: Series, Panel, Hierarchical scitype, same format (see above)

if collection of absolute horizon points is not unique:

type is a pandas DataFrame, with row and col index being time stamps row index corresponds to cutoffs that are predicted from column index corresponds to absolut horizons that are predicted entry is the point prediction of col index predicted from row index entry is nan if no prediction is made at that (cutoff, horizon) pair

update_predict_single(y=None, fh=None, X=None, update_params=True)[source]#

Update model with new data and make forecasts.

This method is useful for updating and making forecasts in a single step.

If no estimator-specific update method has been implemented, default fall-back is first update, then predict.

State required:

Requires state to be “fitted”.

Accesses in self:

Fitted model attributes ending in “_”. Pointers to seen data, self._y and self.X self.cutoff, self._is_fitted If update_params=True, model attributes ending in “_”.

Writes to self:

Update self._y and self._X with y and X, by appending rows. Updates self.cutoff and self._cutoff to last index seen in y. If update_params=True,

updates fitted model attributes ending in “_”.

Parameters
ytime series in sktime compatible data container format

Time series to which to fit the forecaster in the update.

y can be in one of the following formats, must be same scitype as in fit: Series scitype: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D)

for vanilla forecasting, one time series

Panel scitype: pd.DataFrame with 2-level row MultiIndex,

3D np.ndarray, list of Series pd.DataFrame, or nested pd.DataFrame for global or panel forecasting

Hierarchical scitype: pd.DataFrame with 3 or more level row MultiIndex

for hierarchical forecasting

Number of columns admissible depend on the “scitype:y” tag:
if self.get_tag(“scitype:y”)==”univariate”:

y must have a single column/variable

if self.get_tag(“scitype:y”)==”multivariate”:

y must have 2 or more columns

if self.get_tag(“scitype:y”)==”both”: no restrictions on columns apply

For further details:

on usage, see forecasting tutorial examples/01_forecasting.ipynb on specification of formats, examples/AA_datatypes_and_datasets.ipynb

fhint, list, np.array or ForecastingHorizon, optional (default=None)

The forecasting horizon encoding the time stamps to forecast at. if has not been passed in fit, must be passed, not optional

Xtime series in sktime compatible format, optional (default=None)

Exogeneous time series for updating and forecasting

Should be of same scitype (Series, Panel, or Hierarchical) as y if self.get_tag(“X-y-must-have-same-index”),

X.index must contain y.index and fh.index both

update_paramsbool, optional (default=False)
Returns
y_predtime series in sktime compatible data container format

Point forecasts at fh, with same index as fh if fh was relative, index is relative to cutoff after update with y y_pred has same type as the y that has been passed most recently:

Series, Panel, Hierarchical scitype, same format (see above)