Forecasting zero-inflated price changes with a Markov switching mixture model for autoregressive and heteroscedastic time series

The weekly changes in prices of several German milk-based commodities exhibit not only traditional patterns such as mean dependence and volatility clustering, but also a high frequency of zero changes that cannot be explained by well-known ARIMA-GARCH models. We therefore develop a new mixture model which combines the elements of zero-inflated models that are common in microeconometrics and intermittent demand forecasting with a traditional ARIMA(1,1,0)-GARCH(1,1) model. We describe the model components, the data generation processes, the maximum likelihood estimation techniques, and the generation of forecasting distributions and point forecasts by resampling techniques. The model is applied to a low frequency weekly time series of skimmed whey powder (SWP). Competing submodels are compared using the Akaike information criterion (AIC). Furthermore, in addition to the evaluation of the out-of-sample forecasting performance, several coverage and independence tests are also computed.