On a threshold autoregression with conditional heteroscedastic variances

Abstract

This paper considers a time series model with a piecewise linear conditional mean and a piecewise linear conditional variance which is a natural extension of Tong's threshold autoregressive model. The model has potential applications in modelling asymmetric behaviour in volatility in the financial market. Conditions for stationarity and ergodicity are derived. Asymptotic properties of the maximum likelihood estimator and two model diagnostic checking statistics are also presented. An illustrative example based on the Hong Kong Hang Seng index is also reported.