Modelling financial time series with threshold nonlinearity in returns and trading volume

This paper investigates the effect of past returns and trading volumes on the temporal behaviour of international market returns. We propose a class of nonlinear threshold time‐series models with generalized autoregressive conditional heteroscedastic disturbances. Using Bayesian approach, an implementation of Markov chain Monte Carlo procedure is used to obtain estimates of unknown parameters. The proposed family of models incorporates changes in log of volumes in the sense of regime changes and asymmetric effects on the volatility functions. The results show that when differences of log volumes are involved in the system of log return and volatility models, an optimum selection can be achieved. In all the five markets considered, both mean and variance equations involve volumes in the best models selected. Our best models produce higher posterior‐odds ratios than that in Gerlach et al.'s (Phys. A Statist. Mech. Appl. 2006; 360:422–444) models, indicating that our return–volume partition of regimes can offer extra gain in explaining return‐volatility term structure. Copyright © 2007 John Wiley & Sons, Ltd.