Extended switching regression models with time-varying probabilities for combining forecasts

This paper introduces a new methodology, which extends the well-known switching regression model. The extension is via the introduction of several latent state variables, each one of which influencing a disjoint set of the model parameters. Furthermore, the probability distribution of the state variables is allowed to vary over time. This model is called the time varying extended switching regression (TV-ESR) model. The model is used to combine volatility forecasts of several currencies (JPY/USD, GBP/USD, and CHF/USD). A detailed comparison of the forecasts generated by the TV-ESR approach is made with those of traditional linear combining procedures and other methods for combining forecasts derived from the switching regression model. On the basis of out-of-sample forecast encompassing tests as well as other measures for forecasting accuracy, results indicate that the use of this new method yields overall better forecasts than those generated by competing models.