Alternate Forecast: a GMM based representation of forecast and prediction interval

Abstract

Prediction interval represents uncertainty associated with a forecast. The uncertainty has two origins, parameter estimation uncertainty, and parameter estimation bias. The former is generally attributed to the data size used to estimate the model parameters, while the latter capture bias in the training. The unimodal distribution assumption of the prediction interval is key to devising computationally efficient prediction interval estimation. But, this assumption often fails in a non-linear forecasting setup. In this work, we represent an efficient Gaussian Mixture Model-based prediction interval representation, capable of addressing this issue. Each mixture component represents an alternate forecast with associated uncertainty.