PolynomialTrendForecaster
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.
Quickstart
from sktime.forecasting.trend import PolynomialTrendForecaster
estimator = PolynomialTrendForecaster(regressor=None, degree=1, with_intercept=True, prediction_intervals=False)Parameters(4)
- 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.
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 ])References
Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles
and practice, 3rd edition. OTexts: Melbourne, Australia. OTexts.com/fpp3.