Asymptotic Normality for Weighted Sums of Linear Processes

24 Pages Posted: 15 Jan 2012

See all articles by Karim M. Abadir

Karim M. Abadir

Imperial College Business School

Walter Distaso

Imperial College Business School

Liudas Giraitis

University of York - Department of Mathematics and Economics

Hira Koul

Michigan State University

Date Written: January 14, 2012

Abstract

We establish asymptotic normality of weighted sums of stationary linear processes with general triangular array weights and when the innovations in the linear process are martingale differences. The results are obtained under minimal conditions on the weights and as long as the process of conditional variances of innovations is covariance stationary with lag k auto-covariances tending to zero, as k tends to infinity. We also obtain weak convergence of weighted partial sum processes. The results are applicable to linear processes that have short or long memory or exhibit seasonal long memory behavior. In particular they are applicable to GARCH and ARCH(∞) models. They are also useful in deriving asymptotic normality of kernel type estimators of a nonparametric regression function when errors may have long memory.

Suggested Citation

Abadir, Karim M. and Distaso, Walter and Giraitis, Liudas and Koul, Hira, Asymptotic Normality for Weighted Sums of Linear Processes (January 14, 2012). Available at SSRN: https://ssrn.com/abstract=1985281 or http://dx.doi.org/10.2139/ssrn.1985281

Karim M. Abadir (Contact Author)

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/portal/page?_pageid=61,629646&_dad=portallive&_schema=PORTALLIVE

Walter Distaso

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

Liudas Giraitis

University of York - Department of Mathematics and Economics ( email )

Heslington, York YO10 5DD
United Kingdom

Hira Koul

Michigan State University ( email )

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