Long- and short-range dependent sequences under exponential subordination

Lesl aw Gajek and Jan Mielniczuk

Statistics & Probability Letters, 1999, vol. 43, issue 2, 113-121

Abstract: We consider a strictly stationary long-range-dependent process (Zi)i=1[infinity] with standard exponential marginals and its subordinated process (G(Zi))i=1[infinity] for some real function G. We prove that, analogously to the case of Gaussian subordination, the asymptotic behaviour of partial-sum process of a long-range-dependent sequence (G(Zi))i=1[infinity] is the same as that of the first nonvanishing term of its Laguerre expansion (Lm(Zi))i=1[infinity]. Furthermore, convergence in distribution of partial-sum process to a linear combination of generalized Hermite processes of rank 2m is shown. This leads to noncentral limit theorems for an empirical process and kernel density estimators. A parallel problem of convergence in distribution for partial sums of a short-range-dependent exponentially subordinated process to a constant multiple of Wiener process is solved for G having finite Laguerre expansion.

Keywords: Long-range-dependence; Exponential; subordination; Laguerre; expansion; Partial-sum; process (search for similar items in EconPapers)
Date: 1999
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