Giraitis, Liudas ; Surgailis, Donatas
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Abstract
A central limit theorem for the normalized empirical process, basedon a (non-Gaussian) moving average sequence X_t , t in Z, with long memory,is established, generalizing the results of Dehling and Taqqu (1989). The proof is based on the (Appell) expansion 1(X_t <= x) = F(x) + f(x) X_t + ...of the indicator function, where F(x) = P[X_t <= x] is the marginaldistribution function, f(x) = F'(x), and the covariance of the remainder termdecays faster than the covariance of X_t. As a consequence, the limitdistribution of M-functionals and U-statistics based on such long memoryobservations is obtained.
| Document type: | Working paper |
|---|---|
| Place of Publication: | Heidelberg |
| Date Deposited: | 13 Jun 2016 09:05 |
| Date: | December 1994 |
| Number of Pages: | 14 |
| Faculties / Institutes: | The Faculty of Mathematics and Computer Science > Institut für Mathematik |
| DDC-classification: | 510 Mathematics |
| Series: | Beiträge zur Statistik > Beiträge |
