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The functional central limit theorem for the multivariate MS–ARMA–GARCH model

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  • Lee, Oesook
  • Lee, Jungwha

Abstract

In this paper, we consider the multivariate ARMA–GARCH process governed by Markov switching coefficients. We show under proper assumptions that the process holds the L2-NED property and obeys the multivariate functional central limit theorem. The multivariate Markov switching constant conditional correlation(CCC)-GARCH model is considered as a special case.

Suggested Citation

  • Lee, Oesook & Lee, Jungwha, 2014. "The functional central limit theorem for the multivariate MS–ARMA–GARCH model," Economics Letters, Elsevier, vol. 125(3), pages 331-335.
    • Handle: RePEc:eee:ecolet:v:125:y:2014:i:3:p:331-335
    DOI: 10.1016/j.econlet.2014.10.002
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    References listed on IDEAS

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    1. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    2. Francq, Christian & ZakoI¨an, Jean-Michel, 2005. "The L2-structures of standard and switching-regime GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1557-1582, September.
    3. Herrndorf, Norbert, 1984. "A functional central limit theorem for [varrho]-mixing sequences," Journal of Multivariate Analysis, Elsevier, vol. 15(1), pages 141-146, August.
    4. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    5. Lee, O., 2013. "The functional central limit theorem for ARMA–GARCH processes," Economics Letters, Elsevier, vol. 121(3), pages 432-435.
    6. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    7. Berkes, István & Hörmann, Siegfried & Horváth, Lajos, 2008. "The functional central limit theorem for a family of GARCH observations with applications," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2725-2730, November.
    8. Stelzer, Robert, 2009. "On Markov-Switching Arma Processes—Stationarity, Existence Of Moments, And Geometric Ergodicity," Econometric Theory, Cambridge University Press, vol. 25(1), pages 43-62, February.
    9. Davidson, James, 2002. "Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 243-269, February.
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    Cited by:

    1. Asai, M. & Peiris, S. & McAleer, M.J. & Allen, D.E., 2018. "Cointegrated Dynamics for A Generalized Long Memory Process," Econometric Institute Research Papers EI 2018-32, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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    More about this item

    Keywords

    Functional central limit theorem; L2-NED; Multivariate MS–GARCH; Multivariate MS–ARMA–GARCH;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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