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Asymptotic normality for weighted sums of linear processes

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Title: Asymptotic normality for weighted sums of linear processes
Authors: Abadir, KM
Distaso, W
Giraitis, L
Koul, HL
Item Type: Journal Article
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.
Issue Date: 1-Feb-2014
Date of Acceptance: 1-Aug-2013
URI: http://hdl.handle.net/10044/1/15602
DOI: 10.1017/S0266466613000182
ISSN: 0266-4666
Publisher: Cambridge University Press
Start Page: 252
End Page: 284
Journal / Book Title: Econometric Theory
Volume: 30
Issue: 1
Copyright Statement: Copyright © Cambridge University Press 2013 . The final publication is available via Cambride Journals Online at http://dx.doi.org/10.1017/S0266466613000182
Sponsor/Funder: Economic & Social Research Council (ESRC)
Funder's Grant Number: ES/F015909/1
Keywords: Social Sciences
Science & Technology
Physical Sciences
Economics
Mathematics, Interdisciplinary Applications
Social Sciences, Mathematical Methods
Statistics & Probability
Business & Economics
Mathematics
Mathematical Methods In Social Sciences
CENTRAL-LIMIT-THEOREM
FRACTIONAL BROWNIAN-MOTION
AUTOREGRESSIVE TIME-SERIES
UNIT-ROOT
CONDITIONAL HETEROSKEDASTICITY
STOCHASTIC VOLATILITY
INVARIANCE-PRINCIPLE
STATIONARY-PROCESSES
REGRESSION
MODELS
0104 Statistics
1403 Econometrics
Econometrics
Publication Status: Published
Appears in Collections:Imperial College Business School
Grantham Institute for Climate Change
Faculty of Natural Sciences