# ARIMA#

class ARIMA(order=(1, 0, 0), seasonal_order=(0, 0, 0, 0), start_params=None, method='lbfgs', maxiter=50, suppress_warnings=False, out_of_sample_size=0, scoring='mse', scoring_args=None, trend=None, with_intercept=True, time_varying_regression=False, enforce_stationarity=True, enforce_invertibility=True, simple_differencing=False, measurement_error=False, mle_regression=True, hamilton_representation=False, concentrate_scale=False)[source]#

Wrapper of the pmdarima implementation of fitting (S)ARIMA(X) models.

Exposes pmdarima.arima.ARIMA [1] under the sktime interface. Seasonal ARIMA models and exogeneous input is supported, hence this estimator is capable of fitting SARIMA, ARIMAX, and SARIMAX. To additionally fit (S)ARIMA(X) hyper-parameters, use the AutoARIMA estimator.

An ARIMA, or autoregressive integrated moving average model, is a generalization of an autoregressive moving average (ARMA) model, and is fitted to time-series data in an effort to forecast future points. ARIMA models can be especially efficacious in cases where data shows evidence of non-stationarity.

The “AR” part of ARIMA indicates that the evolving variable of interest is regressed on its own lagged (i.e., prior observed) values. The “MA” part indicates that the regression error is actually a linear combination of error terms whose values occurred contemporaneously and at various times in the past. The “I” (for “integrated”) indicates that the data values have been replaced with the difference between their values and the previous values (and this differencing process may have been performed more than once). The purpose of each of these features is to make the model fit the data as well as possible.

Non-seasonal ARIMA models are generally denoted ARIMA(p,d,q) where parameters p, d, and q are non-negative integers, p is the order (number of time lags) of the autoregressive model, d is the degree of differencing (the number of times the data have had past values subtracted), and q is the order of the moving-average model. Seasonal ARIMA models are usually denoted ARIMA(p,d,q)(P,D,Q)m, where m refers to the number of periods in each season, and the uppercase P, D, Q refer to the autoregressive, differencing, and moving average terms for the seasonal part of the ARIMA model.

When two out of the three terms are zeros, the model may be referred to based on the non-zero parameter, dropping “AR”, “I” or “MA” from the acronym describing the model. For example, ARIMA(1,0,0) is AR(1), ARIMA(0,1,0) is I(1), and ARIMA(0,0,1) is MA(1).

See notes for more practical information on the ARIMA class.

Parameters
orderiterable or array-like, shape=(3,), optional (default=(1, 0, 0))

The (p,d,q) order of the model for the number of AR parameters, differences, and MA parameters to use. p is the order (number of time lags) of the auto-regressive model, and is a non-negative integer. d is the degree of differencing (the number of times the data have had past values subtracted), and is a non-negative integer. q is the order of the moving-average model, and is a non-negative integer. Default is an AR(1) model: (1,0,0).

seasonal_orderarray-like, shape=(4,), optional (default=(0, 0, 0, 0))

The (P,D,Q,s) order of the seasonal component of the model for the AR parameters, differences, MA parameters, and periodicity. D must be an integer indicating the integration order of the process, while P and Q may either be an integers indicating the AR and MA orders (so that all lags up to those orders are included) or else iterables giving specific AR and / or MA lags to include. S is an integer giving the periodicity (number of periods in season), often it is 4 for quarterly data or 12 for monthly data. Default is no seasonal effect.

start_paramsarray-like, optional (default=None)

Starting parameters for ARMA(p,q). If None, the default is given by ARMA._fit_start_params.

methodstr, optional (default=’lbfgs’)

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. These can be passed as **fit_kwargs

maxiterint, optional (default=50)

The maximum number of function evaluations. Default is 50

suppress_warningsbool, optional (default=False)

Many warnings might be thrown inside of statsmodels. If suppress_warnings is True, all of these warnings will be squelched.

out_of_sample_sizeint, optional (default=0)

The number of examples from the tail of the time series to hold out and use as validation examples. The model will not be fit on these samples, but the observations will be added into the model’s endog and exog arrays so that future forecast values originate from the end of the endogenous vector. See update. For instance:

y = [0, 1, 2, 3, 4, 5, 6]
out_of_sample_size = 2
> Fit on: [0, 1, 2, 3, 4]
> Score on: [5, 6]
> Append [5, 6] to end of self.arima_res_.data.endog values
scoringstr or callable, optional (default=’mse’)

If performing validation (i.e., if out_of_sample_size > 0), the metric to use for scoring the out-of-sample data:

• If a string, must be a valid metric name importable from sklearn.metrics

• If a callable, must adhere to the function signature:

def foo_loss(y_true, y_pred)

Note that models are selected by minimizing loss. If using a maximizing metric (such as sklearn.metrics.r2_score), it is the user’s responsibility to wrap the function such that it returns a negative value for minimizing.

scoring_argsdict, optional (default=None)

A dictionary of key-word arguments to be passed to the scoring metric.

trendstr or None, optional (default=None)

The trend parameter. If with_intercept is True, trend will be used. If with_intercept is False, the trend will be set to a no- intercept value. If None and with_intercept, ‘c’ will be used as a default.

with_interceptbool, optional (default=True)

Whether to include an intercept term. Default is True.

Further arguments to pass to the SARIMAX constructor:
- time_varying_regressionboolean, optional (default=False)

Whether or not coefficients on the exogenous regressors are allowed to vary over time.

- enforce_stationarityboolean, optional (default=True)

Whether or not to transform the AR parameters to enforce stationarity in the auto-regressive component of the model. - enforce_invertibility : boolean, optional (default=True) Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model.

- simple_differencingboolean, optional (default=False)

Whether or not to use partially conditional maximum likelihood estimation for seasonal ARIMA models. If True, differencing is performed prior to estimation, which discards the first $$s D + d$$ initial rows but results in a smaller state-space formulation. If False, the full SARIMAX model is put in state-space form so that all datapoints can be used in estimation. Default is False.

- measurement_error: boolean, optional (default=False)

Whether or not to assume the endogenous observations endog were measured with error. Default is False.

- mle_regressionboolean, optional (default=True)

Whether or not to use estimate the regression coefficients for the exogenous variables as part of maximum likelihood estimation or through the Kalman filter (i.e. recursive least squares). If time_varying_regression is True, this must be set to False. Default is True.

- hamilton_representationboolean, optional (default=False)

Whether or not to use the Hamilton representation of an ARMA process (if True) or the Harvey representation (if False). Default is False.

- concentrate_scaleboolean, optional (default=False)

Whether or not to concentrate the scale (variance of the error term) out of the likelihood. This reduces the number of parameters estimated by maximum likelihood by one, but standard errors will then not be available for the scale parameter.

Attributes
cutoff

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

fh

Forecasting horizon that was passed.

is_fitted

Whether fit has been called.

AutoARIMA

References

1

https://alkaline-ml.com/pmdarima/modules/generated/pmdarima.arima.ARIMA.html

2

https://www.statsmodels.org/stable/generated/statsmodels.tsa.statespace.sarimax.SARIMAX.html

Examples

>>> from sktime.datasets import load_airline
>>> from sktime.forecasting.arima import ARIMA
>>> y = load_airline()
>>> forecaster = ARIMA(
...     order=(1, 1, 0),
...     seasonal_order=(0, 1, 0, 12),
...     suppress_warnings=True)
>>> forecaster.fit(y)
ARIMA(...)
>>> y_pred = forecaster.predict(fh=[1,2,3])

Methods

 Check if the estimator has been fitted. clone() 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() 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. 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() 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. summary() Summary of the fitted model. 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.
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
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

Default/fallback value if tag is not found.

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

Default/fallback value if tag is not found

raise_errorbool

whether a ValueError is raised when the tag is not found

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.

Load object from file location.

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.

summary()[source]#

Summary of the fitted model.

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)