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Estimation of time-varying ARMA models with Markovian changes in regime

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  • Francq, Christian
  • Gautier, Antony

Abstract

In this paper, we consider the estimation of time-varying ARMA models subject to Markovian changes in regime. We give explicit conditions ensuring consistency and asymptotic normality, as well as the limiting covariance matrix, of least squares and quasi-generalized least-squares estimators.

Suggested Citation

  • Francq, Christian & Gautier, Antony, 2004. "Estimation of time-varying ARMA models with Markovian changes in regime," Statistics & Probability Letters, Elsevier, vol. 70(4), pages 243-251, December.
    • Handle: RePEc:eee:stapro:v:70:y:2004:i:4:p:243-251
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    References listed on IDEAS

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    1. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    2. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    3. Abdelouahab Bibi & Christian Francq, 2003. "Consistent and asymptotically normal estimators for cyclically time-dependent linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 41-68, March.
    4. I. V. Basawa & Robert Lund, 2001. "Large Sample Properties of Parameter Estimates for Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(6), pages 651-663, November.
    5. Robert E. McCulloch & Ruey S. Tsay, 1994. "Statistical Analysis Of Economic Time Series Via Markov Switching Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 523-539, September.
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    Cited by:

    1. Mélard, Guy, 2022. "An indirect proof for the asymptotic properties of VARMA model estimators," Econometrics and Statistics, Elsevier, vol. 21(C), pages 96-111.
    2. Rajae Azrak & Guy Melard, 2017. "Autoregressive Models with Time-dependent Coefficients. A comparison between Several Approaches," Working Papers ECARES ECARES 2017-48, ULB -- Universite Libre de Bruxelles.
    3. Rajae Azrak & Guy Mélard, 2022. "Autoregressive Models with Time-Dependent Coefficients—A Comparison between Several Approaches," Stats, MDPI, vol. 5(3), pages 1-21, August.
    4. Quentin Giai Gianetto & Hamdi Raïssi, 2015. "Testing Instantaneous Causality in Presence of Nonconstant Unconditional Covariance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 46-53, January.
    5. Landy Rabehasaina & Jae-Kyung Woo, 2020. "Analysis of the infinite server queues with semi-Markovian multivariate discounted inputs," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 393-420, April.
    6. repec:dau:papers:123456789/5529 is not listed on IDEAS
    7. Guy Melard, 2020. "An Indirect Proof for the Asymptotic Properties of VARMA Model Estimators," Working Papers ECARES 2020-10, ULB -- Universite Libre de Bruxelles.
    8. 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.
    9. Nazim Regnard & Jean‐Michel Zakoïan, 2010. "Structure and estimation of a class of nonstationary yet nonexplosive GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 348-364, September.
    10. Karanasos, Menelaos & Paraskevopoulos,Alexandros & Canepa, Alessandra, 2020. "Unified Theory for the Large Family of Time Varying Models with Arma Representations: One Solution Fits All," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202008, University of Turin.
    11. repec:dau:papers:123456789/2285 is not listed on IDEAS
    12. Regnard, Nazim & Zakoïan, Jean-Michel, 2011. "A conditionally heteroskedastic model with time-varying coefficients for daily gas spot prices," Energy Economics, Elsevier, vol. 33(6), pages 1240-1251.
    13. repec:dau:papers:123456789/2603 is not listed on IDEAS

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