Bayesian Analysis of a Threshold Stochastic Volatility Model

Posted: 31 Mar 2013

See all articles by Tony S. Wirjanto

Tony S. Wirjanto

University of Waterloo - School of Accounting and Finance; University of Waterloo, Department of Statistics & Actuarial Science

Adam Kolkiewicz

Independent

Zhongxian Men

Independent

Date Written: March 28, 2013

Abstract

This paper proposes a parsimonious threshold stochastic volatility (SV) model for financial asset returns. Instead of imposing a threshold value on the dynamics of the latent volatility process of the SV model, we assume that the innovation of the mean equation follows a threshold distribution in which the mean innovation switches between two regimes. In our model, the threshold is treated as an unknown parameter. We show that the proposed threshold SV model not only can capture the time-varying volatility of returns, but also can accommodate the asymmetric shape of conditional distribution of the returns. Parameter estimation is carried out by using Markov Chain Monte Carlo methods. For model selection and volatility forecast, an auxiliary particle filter technique is employed to approximate the filter and prediction distributions of the returns. Several experiments are conducted to assess the robustness of the proposed model and estimation methods. In the empirical study, we apply our threshold SV model to three return time series. The empirical analysis results show that the threshold parameter has a nonzero value and the mean innovations belong to two separately distinct regimes. We also find that the model with an unknown threshold parameter value consistently outperforms the model with a known threshold parameter value.

Keywords: Threshold Stochastic Volatility, Bayesian Inference, MCMC, Deviance Information Criteria

JEL Classification: C1, C11, C15, G1

Suggested Citation

Wirjanto, Tony S. and Kolkiewicz, Adam and Men, Zhongxian, Bayesian Analysis of a Threshold Stochastic Volatility Model (March 28, 2013). Available at SSRN: https://ssrn.com/abstract=2241193

Tony S. Wirjanto (Contact Author)

University of Waterloo - School of Accounting and Finance ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Canada
519-888-4567 x35210 (Phone)

HOME PAGE: http://https://uwaterloo.ca/statistics-and-actuarial-science/people-profiles/tony-wirjanto

University of Waterloo, Department of Statistics & Actuarial Science ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Canada
519-888-4567 x35210 (Phone)
519-746-1875 (Fax)

HOME PAGE: http://math.uwaterloo.ca/statistics-and-actuarial-science/people-profiles/tony-wirjanto

Adam Kolkiewicz

Independent ( email )

Zhongxian Men

Independent ( email )

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