Markov Switching SV Processes in Modelling Volatility of Financial Time Series

Łukasz Kwiatkowski

doi:https://doi.org/10.59139/ps.2009.01.9

Łukasz Kwiatkowski Krakowska Akademia im. Andrzeja Frycza Modrzewskiego Przegląd Statystyczny. Statistical Review, vol. 56, 2009, 1, pages: 147-168 Published online: 31 March 2009 DOI https://doi.org/10.59139/ps.2009.01.9

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ABSTRACT

This paper presents a Markov Switching Stochastic Volatility model (MSSV) as a specification of potential use in financial econometrics. The model may be viewed as a specific generalization of a wellknown SV construction, that allows the parameters of the conditional volatility equation to switch between a predetermined number of states (regimes). The switching mechanism is driven by a homogenous discrete Markov chain. Without significant loss of generality we restrict our analysis to two regimes only. Then we concentrate on the estimation procedure of a MSSV model, based on the Quasi-Maximum Likelihood approach presented by Smith in [18]. In order to calculate the quasi-log-likelihood function we consider a linear state-space representation of the MSSV model and employ a combination of the Kalman filter and Hamilton’s filter procedures. Finally, four MSSV models and a standard SV model are estimated and compared in terms of goodness of fit to the 1-month WIBOR interest rates.

KEYWORDS

Markov switching, stochastic volatility, quasi-maximum likelihood estimation

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