Markov Chain Monte Carlo Methods for Parameter Estimation in Multidimensional Continuous Time Markov Switching Models

Posted: 28 Dec 2009

See all articles by Markus Hahn

Markus Hahn

affiliation not provided to SSRN

Sylvia Fruhwirth-Schnatter

Johannes Kepler University - Department of Applied Statistics and Econometrics

Jörn Sass

University of Kaiserslautern

Date Written: Winter 2010

Abstract

We consider a multidimensional, continuous-time model where the observation process is a diffusion with drift and volatility coefficients being modeled as continuous-time, finite-state Markov chains with a common state process. For the econometric estimation of the states for drift and volatility and the rate matrix of the underlying Markov chain, we develop both an exact continuous time and an approximate discrete-time Markov chain Monte Carlo (MCMC) sampler and compare these approaches with maximum likelihood (ML) estimation. For simulated data, MCMC outperforms ML estimation for difficult cases like high rates. Finally, for daily stock index quotes from Argentina, Brazil, Mexico, and the USA we identify four states differing not only in the volatility of the various assets but also in their correlation.

Keywords: C11, C13, C15, C32, Bayesian inference, data augmentation, hidden Markov model, switching diffusion

Suggested Citation

Hahn, Markus and Fruhwirth-Schnatter, Sylvia and Sass, Jörn, Markov Chain Monte Carlo Methods for Parameter Estimation in Multidimensional Continuous Time Markov Switching Models (Winter 2010). Journal of Financial Econometrics, Vol. 8, Issue 1, pp. 88-121, 2010. Available at SSRN: https://ssrn.com/abstract=1528360 or http://dx.doi.org/nbp026

Markus Hahn (Contact Author)

affiliation not provided to SSRN

No Address Available

Sylvia Fruhwirth-Schnatter

Johannes Kepler University - Department of Applied Statistics and Econometrics ( email )

Altenbergerstrasse 69
Linz
Austria

Jörn Sass

University of Kaiserslautern

Paul-Ehrlich-Straße 14
Kaiserslautern, D-67663
Germany

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