Preprint #97-4

Bayesian Analysis of Long Memory Stochastic Volatility Models

by

Nan-Jung Hsu and F. Jay Breidt

Recently, Stochastic Volatility (SV) models have been introduced to describe the volatility in returns on financial assets such as stocks. Since many empirical studies have found that stock market volatility exhibits long memory features, we consider estimation for two classes of long memory SV models. One class is constructed from fractionally integrated autoregressive-moving average (ARFIMA) models and the other is constructed from semi-Markov processes with heavy-tailed interarrival times. The exact likelihood of SV models involves an integral with dimension equal to the number of observations and therefore it is very difficult to evaluate. In this paper, posterior inferences on the model parameters and volatilities are obtained via the Gibbs sampling technique. An example is given to demonstrate the methodology.

Keywords: ARFIMA; Gibbs sampler; Pareto distribution; Semi-Markov.


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