Statistical Methodology 6 (2009) 189–201 Contents lists available at ScienceDirect Statistical Methodology journal homepage: www.elsevier.com/locate/stamet Bayesian unit-root tests for Stochastic Volatility models Zeynep I. Kalaylıoğlu a , Sujit K. Ghosh b,* a Department of Statistics, Middle East Technical University, Ankara, Turkey b Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, USA article info Article history: Received 23 April 2007 Received in revised form 10 May 2008 Accepted 25 July 2008 Keywords: BUGS software Gibbs sampling Markov Chain Monte Carlo Stochastic Volatility models Unit-root test abstract In this article, we consider Bayesian inference procedures to test for a unit root in Stochastic Volatility (SV) models. Unit-root tests for the persistence parameter of the SV models, based on the Bayes Factor (BF), have been recently introduced in the literature. In contrast, we propose a flexible class of priors that is non- informative over the entire support of the persistence parameter (including the non-stationarity region). In addition, we show that our model fitting procedure is computationally efficient (using the software WinBUGS). Finally, we show that our proposed test procedures have good frequentist properties in terms of achieving high statistical power, while maintaining low total error rates. We illustrate the above features of our method by extensive simulation studies, followed by an application to a real data set on exchange rates. © 2008 Elsevier B.V. All rights reserved. 1. Introduction In finance, it is very common to see that the mean corrected return on holding an asset has time dependent variation (i.e. volatility). Researchers have been interested in modeling the time dependent feature of unobserved volatility. A model that is commonly used to model such features, is known as the Autoregressive Conditional Heteroscedastic (ARCH) model (see [4]). An extension is to consider Generalized ARCH (GARCH) models, which have been found very popular to model the volatility over time. There is an extensive literature on estimation and testing procedures for GARCH models (e.g., see [2]). However, in ARCH and GARCH models, given the past observations (returns), volatility is a deterministic function of the past observations. This feature may not be appropriate for some real * Corresponding author. Tel.: +1 9195151950; fax: +1 9195157591. E-mail addresses: kzeynep@metu.edu.tr (Z.I. Kalaylıoğlu), ghosh@stat.ncsu.edu (S.K. Ghosh). 1572-3127/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.stamet.2008.07.002