A Mixture Innovation Heterogeneous Autoregressive Model for Structural Breaks and Long Memory

We propose a flexible model that is able to simultaneously approximate long memory behavior as well as incorporate structural breaks in the model parameters. Our model is an extension of the heterogeneous autoregressive (HAR) model, which is designed to model and forecast volatility of financial time series. In an extensive empirical evaluation involving several volatility series, we demonstrate presence of structural breaks and their importance for forecasting. Furthermore, we find that the choice of how to model break processes is important in achieving good forecast performance.