SquaringResiduals

SquaringResiduals

class SquaringResiduals(forecaster=None, residual_forecaster=None, initial_window=5, strategy='square', distr='norm', distr_kwargs=None)[source]

Compute the prediction variance based on a separate forecaster.

Wraps a forecaster with another residual_forecaster object that allows for quantile and interval estimation by fitting the residual_forecaster to the rolling residuals.

Fitting proceeds as follows: Let \(t_1, \dots, t_N\) be the train set. Let steps_ahead be a positive integer indicating the steps ahead we want to forecast the residuals. Let initial_window be the minimal number of observations to which the forecaster is fitted.

1. For \(i = initial\_window, \dots, N - steps\_ahead\)

   1. Train/Update forecaster A on \(y(t_1), \dots, y(t_i)\)

   2. Make point prediction for \(t_{i+steps\_ahead}\) to get \(\hat{y}(t_{i+steps\_ahead})\)

   3. Compute the residual for \(t_{i+steps\_ahead}\) as \(r(t_{i+steps\_ahead}) := y(t_{i+steps\_ahead}) - \hat{y}(t_{i+steps\_ahead})\)

   4. Compute \(e(t_{i+steps\_ahead}) := h(r(t_{i+steps\_ahead}))\) where \(h(x)\) is given by \(strategy\)

2. Train residual_forecaster on \(e(t_{initial\_window+steps\_ahead}), \dots, e(t_{N})\)

Prediction for \(t_{N+steps\_ahead}\) is done as follows:

1. Use forecaster to predict location param \(\hat{y}(t_{N+steps\_ahead})\)

2. Use residual_forecaster to predict scale param \(e(t_{N+steps\_ahead})\)

3. Calculate prediction intervals based on e.g. normal assumption \(N(\hat{y}(t_{N+steps\_ahead}), e(t_{N+steps\_ahead}))\)

Parameters:

forecastersktime forecaster, BaseForecaster descendant, optional

Estimator to which probabilistic forecasts are being added Default = NaiveForecaster()

residual_forecastersktime forecaster, BaseForecaster descendant, optional

Estimator which is fitted to the residuals of forecaster Default = NaiveForecaster()

initial_windowint, optional, default=2

Size of initial_window to which forecaster is fitted

steps_aheadint, optional, default=1

Steps ahead for which we predict the residuals

strategystr, optional, default=’square’

Function applied to the residuals

distrstr, optional, default=’norm’

Distributional assumption ([“norm”, “laplace”, “t”, “cauchy”])

distr_kwargsdict, optional

Additional arguments required by the distribution

Attributes:

forecaster_sktime forecaster, BaseForecaster descendant

Fitted estimator to which probabilistic forecasts are being added

Examples

>>> from sktime.datasets import load_macroeconomic
>>> from sktime.forecasting.base import ForecastingHorizon
>>> from sktime.forecasting.naive import NaiveForecaster
>>> from sktime.forecasting.theta import ThetaForecaster
>>> from sktime.forecasting.squaring_residuals import SquaringResiduals
>>> fc = NaiveForecaster()
>>> var_fc = ThetaForecaster()
>>> y = load_macroeconomic().realgdp
>>> sqr = SquaringResiduals(forecaster=fc, residual_forecaster=var_fc)
...
>>> fh = ForecastingHorizon(values=[1, 2, 3])
>>> sqr = sqr.fit(y, fh=fh)
>>> pred_interval = sqr.predict_interval(coverage=0.95)

Methods

check_is_fitted([method_name])	Check if the estimator has been fitted.
clone()	Obtain a clone of the object with same hyper-parameters and config.
clone_tags(estimator[, tag_names])	Clone tags from another object as dynamic override.
create_test_instance([parameter_set])	Construct an instance of the class, using first test parameter set.
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, X_pred])	Fit and forecast time series at future horizon.
get_class_tag(tag_name[, tag_value_default])	Get class tag value from class, with tag level inheritance from parents.
get_class_tags()	Get class tags from class, with tag level inheritance from parent classes.
get_config()	Get config flags for self.
get_fitted_params([deep])	Get fitted parameters.
get_param_defaults()	Get object's parameter defaults.
get_param_names([sort])	Get object's parameter names.
get_params([deep])	Get a dict of parameters values for this object.
get_pretrained_params([deep])	Get pretrained parameters of this estimator.
get_tag(tag_name[, tag_value_default, ...])	Get tag value from instance, with tag level inheritance and overrides.
get_tags()	Get tags from instance, with tag level inheritance and overrides.
get_test_params([parameter_set])	Return testing parameter settings for the estimator.
is_composite()	Check if the object is composed of other BaseObjects.
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.
pretrain(y[, X, fh])	Pre-train forecaster on panel (global) data.
reset()	Reset the object to a clean post-init state.
save([path, serialization_format])	Save serialized self to bytes-like object or to (.zip) file.
score(y[, X, fh])	Scores forecast against ground truth, using MAPE (non-symmetric).
set_config(**config_dict)	Set config flags to given values.
set_params(**params)	Set the parameters of this object.
set_random_state([random_state, deep, ...])	Set random_state pseudo-random seed parameters for self.
set_tags(**tag_dict)	Set instance level tag overrides to given values.
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.