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 paper 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.

Particle Gibbs with Ancestor Sampling Methods for Unobserved Component Time Series Models with Heavy Tails, Serial Dependence and Structural Breaks

“…Once we sample h 1:T , we use standard methods and sample each element of θ , see for instance Kim et al (1998) and Chan and Hsiao (2013).…”

“…On the other hand, if we were to use pure Gibbs sampling to estimate the SV model with Student-t distributed errors then we would be forced to follow Chan and Hsiao (2013) and convert the model into a conditionally Gaussian state space model by defining the measurement error in (2.1) as ε t = λ −1/2 t e t where e t ∼ N (0, 1), λ t ∼ IG (v/2, v/2) and has a closed form conditional posterior. We would then follow the steps in Chan and Hsiao (2013) and sample from the augmented posterior,…”

“…We use the exact data and prior settings as Chan and Hsiao (2013). Thus, we ought to be able to compare the performance of PG-AS with traditional Gibbs sampling in a rather easy and intuitive way.…”

“…The aforementioned article uses "pure" Gibbs sampling methods to estimate different stochastic volatility model specifications. We briefly summarize their applications, estimate the same models using PG-AS and compare our results with the results of Chan and Hsiao (2013). The main difference between Gibbs sampling and PG-AS is that where in traditional Gibbs sampling problems we resort to converting nonlinear or non-Gaussian models to linear and Gaussian state space models in order to draw the latent states, in the PG-AS framework we draw these latent states directly using the nonlinear or non-Gaussian framework.…”

“…We start by reproducing the results of Chan and Hsiao (2013) which is a book chapter in Bayesian Inference in the Social Sciences published by John Wiley & Sons. The aforementioned article uses "pure" Gibbs sampling methods to estimate different stochastic volatility model specifications.…”