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Conditional asymmetry in Power ARCH($\infty$) models

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  • Royer, Julien

Abstract

We consider an extension of ARCH($\infty$) models to account for conditional asymmetry in the presence of high persistence. After stating existence and stationarity conditions, this paper develops the statistical inference of such models and proves the consistency and asymptotic distribution of a Quasi Maximum Likelihood estimator. Some particular specifications are studied and we introduce a Portmanteau test of goodness-of-fit. In addition, test procedures for asymmetry and GARCH validity are derived. Finally, we present an application on a set of equity indices to reexamine the preeminence of GARCH(1,1) specifications. We find strong evidence that the short memory feature of such models is not suitable for peripheral assets.

Suggested Citation

  • Royer, Julien, 2021. "Conditional asymmetry in Power ARCH($\infty$) models," MPRA Paper 109118, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:109118
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    File URL: https://mpra.ub.uni-muenchen.de/109118/1/MPRA_paper_109118.pdf
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    References listed on IDEAS

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    1. Francq, Christian & Zakoian, Jean-Michel, 2023. "Local Asymptotic Normality Of General Conditionally Heteroskedastic And Score-Driven Time-Series Models," Econometric Theory, Cambridge University Press, vol. 39(5), pages 1067-1092, October.

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    More about this item

    Keywords

    Quasi Maximum Likelihood Estimation; Moderate memory; Testing parameters on the boundary; Recursive design bootstrap;
    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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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