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On White Noises Driven by Hidden Markov Chains

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  • Christian Francq
  • Michel Roussignol

Abstract

We consider a time series model where the variance of the underlying process depends on the state of a non‐observed Markov chain. Maximum likelihood estimates are shown to be consistent. Estimators with asymptotic Gaussian distribution are proposed. Prediction and identification are also mentioned. This is illustrated by means of real and simulated data sets

Suggested Citation

  • Christian Francq & Michel Roussignol, 1997. "On White Noises Driven by Hidden Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(6), pages 553-578, November.
    • Handle: RePEc:bla:jtsera:v:18:y:1997:i:6:p:553-578
    DOI: 10.1111/1467-9892.00068
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    Cited by:

    1. Francq, Christian & Zakoian, Jean-Michel, 2014. "Estimating multivariate GARCH and stochastic correlation models equation by equation," MPRA Paper 54250, University Library of Munich, Germany.
    2. Yacouba Boubacar Maïnassara & Landy Rabehasaina, 2020. "Estimation of weak ARMA models with regime changes," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 1-52, April.
    3. Mark Fiecas & Jürgen Franke & Rainer von Sachs & Joseph Tadjuidje Kamgaing, 2017. "Shrinkage Estimation for Multivariate Hidden Markov Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 424-435, January.
    4. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    5. Bibi, Abdelouahab & Ghezal, Ahmed, 2015. "Consistency of quasi-maximum likelihood estimator for Markov-switching bilinear time series models," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 192-202.
    6. Edoardo Otranto & Giampiero Gallo, 2002. "A Nonparametric Bayesian Approach To Detect The Number Of Regimes In Markov Switching Models," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 477-496.
    7. Martínez, J. Manuel, 1998. "Caracterización del PIB español a partir de modelos univariantes no lineales," DES - Documentos de Trabajo. Estadística y Econometría. DS 3660, Universidad Carlos III de Madrid. Departamento de Estadística.

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