PolynomialTrendForecaster

class PolynomialTrendForecaster(regressor=None, degree=1, with_intercept=True, prediction_intervals=False)[source]

Forecast time series data with a polynomial trend.

Uses an sklearn regressor specified by the regressor parameter to perform regression on time series values against their corresponding indices, after extraction of polynomial features. Same as TrendForecaster where regressor is pipelined with transformation step PolynomialFeatures(degree, with_intercept) applied to time index, at the start.

In fit, for input time series \((v_i, p(t_i)), i = 1, \dots, T\), where \(v_i\) are values, \(t_i\) are time stamps, and \(p\) is the polynomial feature transform with degree degree, and with/without intercept depending on with_intercept, fits an sklearn model \(v_i = f(p(t_i)) + \epsilon_i\), where \(f\) is the model fitted when regressor.fit is passed X = vector of \(p(t_i)\), and y = vector of \(v_i\).

In predict, for a new time point \(t_*\), predicts \(f(p(t_*))\), where \(f\) is the function as fitted above in fit, and \(p\) is the same polynomial feature transform as above.

Default for regressor is linear regression = sklearn LinearRegression, with default parameters. Default for degree is 1.

If time stamps are pd.DatetimeIndex, fitted coefficients are in units of days since start of 1970. If time stamps are pd.PeriodIndex, coefficients are in units of (full) periods since start of 1970.

Parameters:

regressorsklearn regressor estimator object, default = None: Define the regression model type. If not set, will default to sklearn.linear_model.LinearRegression
degreeint, default = 1: Degree of polynomial function
with_interceptbool, default=True: If true, then include a feature in which all polynomial powers are zero. (i.e. a column of ones, acts as an intercept term in a linear model)
prediction_intervalsbool, default=False: Whether to compute prediction intervals. If True, additional calculations are done during fit to enable prediction intervals to be calculated during predict. The prediction intervals are calculated according to Section 7.9 in [1]. The formulas are standard and are based on an OLS regression model fitted to the data. The formulas in [1] assume a regression with intercept and are modified appropriately if with_intercept is False.

Attributes:

regressor_sklearn regressor estimator object: The fitted regressor object. This is a fitted sklearn pipeline with steps PolynomialFeatures(degree, with_intercept), followed by a clone of regressor.

References

[1]

Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles

and practice, 3rd edition. OTexts: Melbourne, Australia. OTexts.com/fpp3.

Examples

>>> from sktime.datasets import load_airline
>>> from sktime.forecasting.trend import PolynomialTrendForecaster
>>> y = load_airline()
>>> forecaster = PolynomialTrendForecaster(degree=1)
>>> forecaster.fit(y)
PolynomialTrendForecaster(...)
>>> y_pred = forecaster.predict(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.