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Recursive Estimation In Switching Autoregressions With A Markov Regime

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  • Ulla Holst
  • Georg Lindgren
  • Jan Holst
  • Mikael Thuvesholmen

Abstract

. A hidden Markov regime is a Markov process that governs the time or space dependent distributions of an observed stochastic process. We propose a recursive algorithm for parameter estimation in a switching autoregressive process governed by a hidden Markov chain. A common approach to the recursive estimation problem is to base the estimation on suboptimal modifications of Kalman filtering techniques. The main idea in this paper is to use the maximum likelihood method and from this develop a recursive EM algorithm.

Suggested Citation

  • Ulla Holst & Georg Lindgren & Jan Holst & Mikael Thuvesholmen, 1994. "Recursive Estimation In Switching Autoregressions With A Markov Regime," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 489-506, September.
    • Handle: RePEc:bla:jtsera:v:15:y:1994:i:5:p:489-506
    DOI: 10.1111/j.1467-9892.1994.tb00206.x
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    Cited by:

    1. Bergman, U. Michael & Hansson, Jesper, 1999. "Real Exchange Rates and Switching Regimes," Working Papers 1999:4, Lund University, Department of Economics, revised 08 Jun 2000.
    2. Paap, Richard & van Dijk, Herman K, 2003. "Bayes Estimates of Markov Trends in Possibly Cointegrated Series: An Application to U.S. Consumption and Income," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 547-563, October.
    3. Jacobson Tor & Lindh Thomas & Warne Anders, 2002. "Growth, Saving, Financial Markets, and Markov Switching Regimes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(4), pages 1-20, January.
    4. Andrew Ang & Allan Timmermann, 2012. "Regime Changes and Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 313-337, October.
    5. Anders Rygh Swensen, 1997. "Change in Regime and Markov Models," Discussion Papers 204, Statistics Norway, Research Department.
    6. Blix, M, 1997. "Rational Expectations in a VAR with Markov Switching," Papers 627, Stockholm - International Economic Studies.
    7. Wilfling, Bernd, 2009. "Volatility regime-switching in European exchange rates prior to monetary unification," Journal of International Money and Finance, Elsevier, vol. 28(2), pages 240-270, March.
    8. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911, October.
    9. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, October.
    10. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    11. Masaru Chiba, 2023. "Robust and efficient specification tests in Markov-switching autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 99-137, April.
    12. Billio, Monica & Casarin, Roberto & Ravazzolo, Francesco & van Dijk, Herman K., 2012. "Combination schemes for turning point predictions," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(4), pages 402-412.
    13. Allam, Abdelaziz & Mourid, Tahar, 2014. "Covariance operator estimation of a functional autoregressive process with random coefficients," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 1-8.
    14. Chew Lian Chua & Sandy Suardi, 2005. "Is There a Unit Root in East-Asian Short-Term Interest Rates?," Melbourne Institute Working Paper Series wp2005n14, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    15. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    16. Bergman, U. Michael & Hansson, Jesper, 2005. "Real exchange rates and switching regimes," Journal of International Money and Finance, Elsevier, vol. 24(1), pages 121-138, February.
    17. Yao, J., 2001. "On square-integrability of an AR process with Markov switching," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 265-270, April.
    18. Ang, Andrew & Bekaert, Geert, 2002. "Short rate nonlinearities and regime switches," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1243-1274, July.

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