Application in stochastic volatility models of nonlinear regression with stochastic design

In regression model with stochastic design, the observations have been primarily treated as a simple random sample from a bivariate distribution. It is of enormous practical significance to generalize the situation to stochastic processes. En this paper, estimation and hypothesis testing problems in stochastic volatility model are considered, when the volatility depends on a nonlinear function of the state variable of other stochastic process, but the correlation coefficient vertical bar rho vertical bar not equal +/- 1. The methods are applied to estimate the volatility of stock returns from Shanghai stock exchange. Copyright (C) 2009 John Wiley & Sons, Ltd.