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arXiv · 2111.07650

Joint FCLT for Sample Quantile and Measures of Dispersion for Functionals of Mixing Processes

Marcel Bräutigam·Marie Kratz
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Abstract

In this paper, we establish a joint (bivariate) functional central limit theorem of the sample quantile and the $r$-th absolute centred sample moment for functionals of mixing processes. More precisely, we consider $L_2$-near epoch dependent processes that are functionals of either $\phi$-mixing or absolutely regular processes. The general results we obtain can be used for two classes of popular and important processes in applications: The class of augmented GARCH($p$,$q$) processes with independent and identically distributed innovations (including many GARCH variations used in practice) and the class of ARMA($p$,$q$) processes with mixing innovations (including, e.g., ARMA-GARCH processes). For selected examples, we provide exact conditions on the moments and parameters of the process for the joint asymptotics to hold.

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Marcel Bräutigam, Marie Kratz. 2021-11-15. Joint FCLT for Sample Quantile and Measures of Dispersion for Functionals of Mixing Processes. https://arxiv.org/abs/2111.07650

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