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The functional central limit theorem for ARMA–GARCH processes

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  • Lee, O.

Abstract

In this paper, we study the functional central limit theorem for ARMA–GARCH processes. We prove that, under the finite second moment assumption, the stationary ARMA–GARCH process is geometricallyL2-NED and that the functional central limit theorem holds.

Suggested Citation

  • Lee, O., 2013. "The functional central limit theorem for ARMA–GARCH processes," Economics Letters, Elsevier, vol. 121(3), pages 432-435.
    • Handle: RePEc:eee:ecolet:v:121:y:2013:i:3:p:432-435
    DOI: 10.1016/j.econlet.2013.09.018
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    References listed on IDEAS

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    1. 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.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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    6. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    7. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(1), pages 3-22, February.
    8. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    9. Achim Zeileis & Friedrich Leisch & Christian Kleiber & Kurt Hornik, 2005. "Monitoring structural change in dynamic econometric models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(1), pages 99-121, January.
    10. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
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    Cited by:

    1. Blöchlinger, Andreas, 2021. "Interest rate risk in the banking book: A closed-form solution for non-maturity deposits," Journal of Banking & Finance, Elsevier, vol. 125(C).
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    3. 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.
    4. Lee, Oesook, 2018. "Stationarity and functional central limit theorem for ARCH(∞) models," Economics Letters, Elsevier, vol. 162(C), pages 107-111.
    5. Maddalena Cavicchioli, 2021. "Statistical inference for mixture GARCH models with financial application," Computational Statistics, Springer, vol. 36(4), pages 2615-2642, December.

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    More about this item

    Keywords

    Functional central limit theorem; GARCH; ARMA–GARCH; L2-NED;
    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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