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Long- and short-range dependent sequences under exponential subordination

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  • aw Gajek, Lesl
  • Mielniczuk, Jan

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.

Suggested Citation

  • aw Gajek, Lesl & Mielniczuk, Jan, 1999. "Long- and short-range dependent sequences under exponential subordination," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 113-121, June.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:2:p:113-121
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    References listed on IDEAS

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    1. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606, November.
    2. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590, November.
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