"A Generalized SSAR Model and Predictive Distribution with an Application to VaR"

The asymmetrical movements between the downward and upward phases of the sample paths of time series have been sometimes observed. By generalizing the SSAR (simultaneous switching autoregressive) models, we introduce a class of nonlinear time series models having the asymmetrical sample paths in the upward and downward phases. We show that the class of generalized SSAR models is useful for estimating the asymmetrical predictive distribution given the present and past information. Applications to the prediction based on the predictive median and the estimation of the VaR (value at risk) in financial risk management are discussed.