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Limits for the Gaussian QMLE in the Non-Stationary GARCH(1,1) Mod

Author

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  • Stelios Arvanitis

    (Athens University of Economics and Business)

  • Alexandros Louka

    (Athens University of Economics and Business)

Abstract

We derive the limit theory of the Gaussian QMLE in the non-stationary GARCH(1,1) model when the square dinnovation process lies in the domain of attraction of a stable law. Analogously to the stationary case, when the stability parameter lies in (1, 2], we find regularly varying rates and stable limits for the QMLE of the ARCH and GARCH parame- ters.

Suggested Citation

  • Stelios Arvanitis & Alexandros Louka, 2017. "Limits for the Gaussian QMLE in the Non-Stationary GARCH(1,1) Mod," Working Papers 201705, Athens University Of Economics and Business, Department of Economics.
    • Handle: RePEc:aeb:wpaper:201705:y:2017
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    Keywords

    Martingale Limit Theorem; Domain of Attraction; Stable Distribution; Slowly Varying Sequence; Non-Stationarity; Gaussian QMLE; Regularly Varying Rate.;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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