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

ThetaModelResults.prediction_intervals(steps=1, theta=2, alpha=0.05)[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.