Giraitis, Liudas and Surgailis, Donatas (1999) Central limit theorem for the empirical process. Journal of statistical planning and inference, 80 (1-2). pp. 81-93. ISSN 0378-3758
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.
|Additional Information:||© 1999 Elsevier Science B.V.|
|Uncontrolled Keywords:||Long-range dependence; Empirical process; Functional central limit theorem|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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