statsmodels.tsa.forecasting.theta.ThetaModelResults.prediction_intervals¶

ThetaModelResults.prediction_intervals(steps: int = 1, theta: float = 2, alpha: float = 0.05) → pandas.core.frame.DataFrame[source]¶

Parameters

stepsint, default 1: The number of steps ahead to compute the forecast components.
thetafloat, default 2: The theta value to use when computing the weight to combine the trend and the SES forecasts.
alphafloat, default 0.05: Significance level for the confidence intervals.

Returns

DataFrame: DataFrame with columns lower and upper

Notes

The variance of the h-step forecast is assumed to follow from the integrated Moving Average structure of the Theta model, and so is \(\sigma^2(1 + (h-1)(1 + (\alpha-1)^2)\). The prediction interval assumes that innovations are normally distributed.