Central limit theorem for the empirical process of a linear sequence with long memory

被引：41

作者：

Giraitis, L

Surgailis, D

机构：

[1] London Sch Econ, London WC2A 2AE, England

[2] Inst Math & Informat, LT-2600 Vilnius, Lithuania

[3] Siauliai Univ, LT-2600 Vilnius, Lithuania

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 1999年 / 80卷 / 1-2期

关键词：

long-range dependence; empirical process; functional central limit theorem;

D O I：

10.1016/S0378-3758(98)00243-2

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 + delta)-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. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：81 / 93

页数：13

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