Stochastic volatility: likelihood inference and comparison with ARCH models

Stochastic volatility models present a natural way of working with time-varying volatility. However the difficulty involved in estimating these types of models has prevented their wide-spread use in empirical applications. In this paper we exploit Gibbs sampling to provide a likelihood framework for the analysis of stochastic volatility models, demonstrating how to perform either maximum likelihood or Bayesian estimation. The paper includes an extensive Monte Carlo experiment which compares the efficiency of the maximum likelihood estimator with that of quasi-likelihood and Bayesian estimators proposed in the literature. We also compare the fit of the stochastic volatility model to that of ARCH models using the likelihood criterion to illustrate the flexibility of the framework presented.