Forecasting Itô-type Processes Using Features Based on Dynamic Gaussian Mixtures

This paper investigates the forecasting performance of a recently proposed time-series feature extraction method based on moments of finite Gaussian mixtures. We extend this method to use maximum weighted likelihood estimation and give more weight to more recent observations. We use rolling window forward validation and proper scoring rules with bootstrap confidence intervals to check whether mixture moments help lower the average forecast loss of a linear AR(p) model. We find limited evidence of this being the case: models with mixtures moments as additional features reduce the average loss by about 1 $$%$$ .