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

11/15/2021

∙

by   Marcel Bräutigam, et al.

∙

0

∙

share

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 ϕ-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.