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Central limit theorem for the empirical process

By Liudas Giraitis and Donatas Surgailis

Abstract

We discuss the functional central limit theorem (FCLT) for the empirical process of a moving-average stationary sequence with long memory. The cases of one-sided and double-sided moving averages are discussed. In the case of one-sided (causal) moving average, the FCLT is obtained under weak conditions of smoothness of the distribution and the existence of (2+δ)-moment of i.i.d. innovations, by using the martingale difference decomposition due to Ho and Hsing (1996, Ann. Statist. 24, 992–1014). In the case of double-sided moving average, the proof of the FCLT is based on an asymptotic expansion of the bivariate probability density

Topics: QA Mathematics
Publisher: Elsevier
Year: 1999
DOI identifier: 10.1016/S0378-3758(98)00243-2
OAI identifier: oai:eprints.lse.ac.uk:7164
Provided by: LSE Research Online
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