Journal Article

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

Markus Hahn, Sylvia Frühwirth-Schnatter and Jörn Sass

in Journal of Financial Econometrics

Volume 8, issue 1, pages 88-121
Published in print January 2010 | ISSN: 1479-8409
Published online January 2010 | e-ISSN: 1479-8417 | DOI: https://dx.doi.org/10.1093/jjfinec/nbp026
Markov Chain Monte Carlo Methods for Parameter Estimation in Multidimensional Continuous Time Markov Switching Models

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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

Journal Article.  11768 words.  Illustrated.

Subjects: Financial Markets ; Econometrics and Mathematical Economics

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