Estimation of Stochastic Volatility Models with Heavy Tails and Serial Dependence

Abstract

Financial time series often exhibit properties that depart from the usual assumptions of serial independence and normality. These include volatility clustering, heavy-tailedness and serial dependence. A voluminous literature on different approaches for modeling these empirical regularities has emerged in the last decade. In this chapter we review the estimation of a variety of highly flexible stochastic volatility models, and introduce some efficient algorithms based on recent advances in state space simulation techniques. These estimation methods are illustrated via empirical examples involving precious metal and foreign exchange returns. The corresponding MATLAB code is also provided.1 The remaining of the chapter is structured as follows. Section 6.2 first discusses the basic stochastic volatility model and its estimation. In particular, we provide details of the auxiliary mixture sampler and the precision sampler for linear Gaussian state space models. In Section 6.3 we extend the basic stochastic volatility model to allow for moving average errors. We then discuss an efficient estimation method based on fast band matrix routines. Lastly, Section 6.4 considers another extension—instead of the conventional assumption of a Gaussian error distribution, we discuss some heavy-tailed distributions that can be written as scale mixtures of Gaussian distributions. We demonstrate the relevance of these heavy-tailed stochastic volatility models through an empirical example.