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