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The functional central limit theorem for Markov-switching GARCH model

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  • Kwon, Dream
  • Lee, Oesook

Abstract

In this paper we consider the Markov Switching GARCH model suggested by Haas, Mittnik, and Paolella(2004). We show under proper assumptions that the functional central limit theorems hold for the process, the square of the process, and regime variances. The functional central limit theorem for a linear combination of regime variances is also obtained.

Suggested Citation

  • Kwon, Dream & Lee, Oesook, 2024. "The functional central limit theorem for Markov-switching GARCH model," Economics Letters, Elsevier, vol. 238(C).
    • Handle: RePEc:eee:ecolet:v:238:y:2024:i:c:s0165176524002118
    DOI: 10.1016/j.econlet.2024.111728
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    References listed on IDEAS

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    1. Christian Francq & Michel Roussignol & Jean‐Michel Zakoian, 2001. "Conditional Heteroskedasticity Driven by Hidden Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(2), pages 197-220, March.
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    4. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    5. 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.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
    8. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    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.
    10. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Markov switching GARCH model; Functional central limit theorem; ϕ-mixing;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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