A Bayesian conditional autoregressive geometric process model for range data

Extreme value theories indicate that the range is an efficient estimator of local volatility in financial time series. A geometric process (GP) framework that incorporates the conditional autoregressive range (CARR)-type mean function is presented for range data. The proposed model, called the conditional autoregressive geometric process range (CARGPR) model, allows for flexible trend patterns, threshold effects, leverage effects, and long-memory dynamics in financial time series. For robustness considerations, a log-t distribution is adopted. Model implementation can be easily done using the WinBUGS package. A simulation study shows that model parameters are estimated with high accuracy. In the empirical study on the range data of an Australian stock market index, the CARGPR model outperforms the CARR model in both in-sample estimation and out-of-sample forecast.