Bivariate FCLT for the Sample Quantile and Measures of Dispersion for Augmented GARCH(p, q) processes

Bräutigam Marcel and Kratz Marie ()
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Bräutigam Marcel: Sorbonne University
Kratz Marie: ESSEC Research Center, ESSEC Business School, Postal: ESSEC Research Center, BP 105, 95021 Cergy, France

No WP1909, ESSEC Working Papers from ESSEC Research Center, ESSEC Business School

Abstract: In this note, we build upon the asymptotic theory for GARCH processes, considering the general class of augmented GARCH(p, q) processes. Our contribution is to complement the well-known univariate asymptotics by providing a bivariate functional central limit theorem between the sample quantile and the r-th absolute centred sample moment. This extends existing results in the case of identically and independently distributed random variables. We show that the conditions for the convergence of the estimators in the univariate case suffice even for the joint bivariate asymptotics. We illustrate the general results with various specific examples from the class of augmented GARCH(p, q) processes and show explicitly under which conditions on the moments and parameters of the process the joint asymptotics hold.

Keywords: Asymptotic distribution; Sample variance; Functional central limit theorem; Augmented GARCH; Correlation; Sample quantile; Measure of dispersion; Sample mean absolute deviation (search for similar items in EconPapers)
JEL-codes: C13 C14 C30 (search for similar items in EconPapers)
Pages: 15 pages
Date: 2019-06-29
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