Asymptotic Normality for Weighted Sums of Linear Processes
AbstractWe 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 estimators of a nonparametric regression function when errors may have long memory.
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Bibliographic InfoPaper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 23_12.
Date of creation: Jun 2012
Date of revision:
Linear process; weighted sum; Lindeberg-Feller;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-06-25 (All new papers)
- NEP-ECM-2012-06-25 (Econometrics)
- NEP-ETS-2012-06-25 (Econometric Time Series)
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