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ASYMPTOTIC NORMALITY FOR WEIGHTED SUMS OF LINEAR PROCESSES

Published online by Cambridge University Press:  20 August 2013

Karim M. Abadir ,
Walter Distaso ,
Liudas Giraitis  and
Hira L. Koul
Karim M. Abadir
Affiliation:
Imperial College London
Walter Distaso
Affiliation:
Imperial College London
Liudas Giraitis*
Affiliation:
Queen Mary, University of London
Hira L. Koul
Affiliation:
Michigan State University
*
*Address correspondence to Liudas Giraitis, School of Ecnomics and Finance, Queen Mary, University of London, Mile End Rd., London E14NS, United Kingdom; e-mail: [email protected]
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Abstract

We establish asymptotic normality of weighted sums of 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 innovations. 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 and to their squares. They are also useful in deriving asymptotic normality of kernel-type estimators of a nonparametric regression function with short or long memory moving average errors.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 1 , February 2014 , pp. 252 - 284
Copyright
Copyright © Cambridge University Press 2013 

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