%0 Generic
%A Giraitis, Liudas
%A Surgailis, Donatas
%C Heidelberg
%D 1994
%F heidok:20934
%R 10.11588/heidok.00020934
%T A Central Limit Theorem for the Empirical Process of a Long Memory Linear Sequence
%U https://archiv.ub.uni-heidelberg.de/volltextserver/20934/
%X 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.