statsmodels.tsa.forecasting.theta.ThetaModelResults.prediction_intervals

ThetaModelResults.prediction_intervals(steps=1, theta=2, alpha=0.05)[source]
Parameters:

  • steps (int, default 1) – The number of steps ahead to compute the forecast components.

  • theta (float, default 2) – The theta value to use when computing the weight to combine the trend and the SES forecasts.

  • alpha (float, default 0.05) – Significance level for the confidence intervals.

Returns:

DataFrame with columns lower and upper

Return type:

DataFrame

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.