Bayesian Analysis of Stochastic Volatility Models

TLDR

The paper develops new techniques for analyzing stochastic volatility models with autoregressive log‑variance. The authors employ a cyclic Metropolis algorithm to build a Markov‑chain simulation tool, applying it to daily and weekly stock and exchange‑rate data and comparing Bayes estimators with existing methods. Simulations converge to the posterior, yielding exact filtering/smoothing and multistep‑ahead predictive densities, and Bayes estimators outperform method‑of‑moments and quasi‑maximum‑likelihood estimators in estimation and filtering.

Abstract

New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain converge in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance states is a by-product of our Markov-chain method. In addition, multistep-ahead predictive densities can be constructed that reflect both inherent model variability and parameter uncertainty. We illustrate our method by analyzing both daily and weekly data on stock returns and exchange rates. Sampling experiments are conducted to compare the performance of Bayes estimators to method of moments and quasi-maximum likelihood estimators proposed in the literature. In both parameter estimation and filtering, the Bayes estimators outperform these other approaches.