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

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  • Markus Hahn
  • Sylvia Frühwirth-Schnatter
  • Jörn Sass

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. Copyright The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oupjournals.org, Oxford University Press.

Suggested Citation

  • Markus Hahn & Sylvia Frühwirth-Schnatter & Jörn Sass, 2010. "Markov Chain Monte Carlo Methods for Parameter Estimation in Multidimensional Continuous Time Markov Switching Models," Journal of Financial Econometrics, Oxford University Press, vol. 8(1), pages 88-121, Winter.
    • Handle: RePEc:oup:jfinec:v:8:y:2010:i:1:p:88-121
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbp026
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    Citations

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    Cited by:

    1. Rey, Clément & Rey, Serge & Viala, Jean-Renaud, 2014. "Detection of high and low states in stock market returns with MCMC method in a Markov switching model," Economic Modelling, Elsevier, vol. 41(C), pages 145-155.
    2. Massimo Guidolin, 2011. "Markov Switching Models in Empirical Finance," Advances in Econometrics, in: Missing Data Methods: Time-Series Methods and Applications, pages 1-86, Emerald Group Publishing Limited.
    3. Bäuerle Nicole & Gilitschenski Igor & Hanebeck Uwe, 2015. "Exact and approximate hidden Markov chain filters based on discrete observations," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 159-176, December.
    4. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    5. Vikram Krishnamurthy & Elisabeth Leoff & Jorn Sass, 2016. "Filterbased Stochastic Volatility in Continuous-Time Hidden Markov Models," Papers 1602.05323, arXiv.org.
    6. Yarovaya, Larisa & Matkovskyy, Roman & Jalan, Akanksha, 2021. "The effects of a “black swan” event (COVID-19) on herding behavior in cryptocurrency markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 75(C).
    7. Krishnamurthy, Vikram & Leoff, Elisabeth & Sass, Jörn, 2018. "Filterbased stochastic volatility in continuous-time hidden Markov models," Econometrics and Statistics, Elsevier, vol. 6(C), pages 1-21.
    8. Ali Al-Aradi & Sebastian Jaimungal, 2019. "Active and Passive Portfolio Management with Latent Factors," Papers 1903.06928, arXiv.org.
    9. Lux, Thomas, 2013. "Exact solutions for the transient densities of continuous-time Markov switching models: With an application to the poisson multifractal model," Kiel Working Papers 1871, Kiel Institute for the World Economy (IfW Kiel).
    10. Yun Bao & Carl Chiarella & Boda Kang, 2012. "Particle Filters for Markov Switching Stochastic Volatility Models," Research Paper Series 299, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Nicole Bauerle & Igor Gilitschenski & Uwe D. Hanebeck, 2014. "Exact and Approximate Hidden Markov Chain Filters Based on Discrete Observations," Papers 1411.0849, arXiv.org, revised Dec 2014.
    12. BenSaïda, Ahmed, 2015. "The frequency of regime switching in financial market volatility," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 63-79.

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