SEMIPARAMETRIC REPRESENTATION OF A GENERALIZED STOCHASTIC VOLATILITY MODEL AND HIDDEN MARKOV APPROXIMATION

In this paper I propose a discrete hidden Markov model to approximate a general class of stochastic volatility models with homogenous volatility processes, including the popular Ornstein-Uhlenbeck process. The advantage of this model is that it allows for unknown forms of the volatility data-generating process and thus avoids model-selection problems in empirical time series analysis. Estimation and forecast procedures are introduced, and applications on exchange-rate series are evaluated. I find that this model, although requiring greater computational effort, meets various specification tests better than some GARCH models.