NaiveVariance

NaiveVariance

class NaiveVariance(forecaster, initial_window=1, verbose=False)[source]

Compute the prediction variance based on a naive strategy.

NaiveVariance adds to a forecaster the ability to compute the prediction variance based on naive assumptions about the time series. The simple strategy is as follows: - Let \(y_1,\dots,y_T\) be the time series we fit the estimator \(f\) to. - Let \(\widehat{y}_{ij}\) be the forecast for time point \(j\), obtained from fitting the forecaster to the partial time series \(y_1,\dots,y_i\). - We compute the residuals matrix \(R=(r_{ij})=(y_j-\widehat{y}_{ij})\). - The variance prediction \(v_k\) for \(y_{T+k}\) is \(\frac{1}{T-k}\sum_{i=1}^{T-k} a_{i,i+k}^2\) because we are averaging squared residuals of all forecasts that are \(k\) time points ahead. - And for the covariance matrix prediction, the formula becomes \(Cov(y_k, y_l)=\frac{\sum_{i=1}^N \hat{r}_{k,k+i}*\hat{r}_{l,l+i}}{N}\).

The resulting forecaster will implement

predict_interval, predict_quantiles, predict_var, and predict_proba, even if the wrapped forecaster forecaster did not have this capability; for point forecasts (predict), behaves like the wrapped forecaster.

Parameters:

forecasterestimator

Estimator to which probabilistic forecasts are being added

initial_windowint, optional, default=1

number of minimum initial indices to use for fitting when computing residuals

verbosebool, optional, default=False

whether to print warnings if windows with too few data points occur

Attributes:

cutoff

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

fh

Forecasting horizon that was passed.

is_fitted

Whether fit has been called.

state

State of the estimator.

Examples

>>> from sktime.datasets import load_airline
>>> from sktime.forecasting.naive import NaiveForecaster, NaiveVariance
>>> y = load_airline()
>>> forecaster = NaiveForecaster(strategy="drift")
>>> variance_forecaster = NaiveVariance(forecaster)
>>> variance_forecaster.fit(y)
NaiveVariance(...)
>>> var_pred = variance_forecaster.predict_var(fh=[1,2,3])

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.