Łukasz Kwiatkowski

(English) PDF


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.


Markov switching, stochastic volatility, quasi-maximum likelihood estimation


[1] Abramowitz M., Stegun N., [1968], Handbook of Mathematical Functions, Dover Publications, New York.

[2] Bauwens L., Preminger A., Rombouts J., [2006], Regime Switching GARCH Models, Core Discussion Paper, Département des Sciences Économiques de l’Université catholique de Louvain.

[3] Bollerslev T., [1987], Generalised Autoregressive Conditional Heteroskedasticity, „Journal of Econometrics”, Vol. 31.

[4] Carvalho C.M., Lopes H.F., [2006], Simulation-based sequential analysis of Markov switching stochastic volatility models, Computational Statistics & Data Analysis, doi: 10.1016/j.csda.2006.07.019.

[5] Casarin R., [2004], Bayesian Monte Carlo Filtering for Stochastic Volatility Models, Cahier du CEREMADE N. 0415, University Paris Dauphine.

[6] Clark P.K., [1973], A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices, „Econometrica”, Vol. 41.

[7] Diebold F.X., Inoue A., [2001], Long Memory and Regime Switching, Journal of Econometrics, Vol. 105.

[8] Engle R.F., [1982], Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of the United Kingdom Inflation, „Econometrica”, Vol. 50.

[9] Francq C., Zakoian J.-M., [2001], Stationarity of multivariate Markov-switching ARMA models, „Journal of Econometrics”, Vol. 102.

[10] Granger C.W.J., Hyung N., [1999], Occasional Structural Breaks and Long Memory, Discussion Paper 99-14, Department of Economics, University of California, San Diego.

[11] Hamilton J. D. (1989), A New approach to the economic analysis of nonstationary time series and the business cycle, „Econometrica”, Vol. 57, No. 2.

[12] Hwang S., Satchell S.E., Pereira P.L.V., [2003], Stochastic Volatility Models with Markov Regime Switching State Equations, „Journal of Business and Economic Statistics”, Vol. 16, No. 2.

[13] Hwang S., Satchell S.E., Pereira P.L.V., [2004], How Persistent is Volatility? An Answer with Stochastic Volatility Models with Markov Regime Switching State Equations, CEA@Cass Working Paper Series, http://www.cass.city.ac.uk/cea/index.html

[14] Nielsen S., Olesen J.O., [2000], Regime-switching stock returns and mean reversion, Working paper 11-2000, Institut for Nationalokonomi, http://citeseer.ist.psu.edu

[15] Pajor A., [2003], Procesy zmienności stochastycznej SV w bayesowskiej analizie finansowych szeregów czasowych, (Stochastic Volatility Processes in Bayesian Analysis of Financial Time Series), doctoral dissertation (in Polish), Published by Cracow University of Economics, Kraków.

[16] Ruiz E., [1994], Quasi-maximum likelihood estimation of stochastic volatility models, „Journal of Econometrics”, Vol. 63.

[17] Shibata M., Watanabe T., [2005], Bayesian Analysis of a Markov Switching Stochastic Volatility Model, „Journal of the Japan Statistical Society”, Vol. 35, No. 2.

[18] Smith D.R., [2000], Markov-switching and stochastic volatility diffusion models for short-term interest rates, http://citeseer.ist.psu.edu/434894.html

[19] So M.K.P., Lam K., Li W.K., [1998], A stochastic volatility model with Markov switching, „Journal of Business and Economic Statistics”, Vol. 16, No. 2.

Back to top
© 2019–2022 Copyright by Statistics Poland, some rights reserved. Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0) Creative Commons — Attribution-ShareAlike 4.0 International — CC BY-SA 4.0