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Stationarity and functional central limit theorem for ARCH(∞) models

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  • Lee, Oesook

Abstract

In this paper, we study the stationarity and functional central limit theorem for (random coefficient) ARCH(∞) models including HYAPGARCH and mixture memory GARCH models. Those models are able to cover long memory property with fewer parameters and have finite variances. The functional central limit theorems for ut and the squared processes ut2 and σt2 are proved. Sufficient conditions for L2-NED property to hold are established and the FCLT for mixture memory GARCH model as an example of a random coefficient ARCH(∞) process is derived via L2-NED condition.

Suggested Citation

  • Lee, Oesook, 2018. "Stationarity and functional central limit theorem for ARCH(∞) models," Economics Letters, Elsevier, vol. 162(C), pages 107-111.
    • Handle: RePEc:eee:ecolet:v:162:y:2018:i:c:p:107-111
    DOI: 10.1016/j.econlet.2017.11.017
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    References listed on IDEAS

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    More about this item

    Keywords

    Functional central limit theorem; L2-NED property; Mixture memory GARCH process; Random coefficient ARCH(∞) process;
    All these keywords.

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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