Bernoulli

  • Bernoulli
  • Volume 10, Number 2 (2004), 327-355.

Stable limits of sums of bounded functions of long-memory moving averages with finite variance

Donatas Surgailis

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Abstract

We discuss limit distributions of partial sums of bounded functions h of a long-memory moving-average process Xt= ∑j=1 bj ζt-j with coefficients bj decaying as j, 1/2< β< 1, and independent and identically distributed innovations ζs whose probability tails decay as x, 2< α< 4. The case of h having Appell rank k*=2 or 3 is discussed in detail. We show that in this case and in the parameter region αβ< 2 , the partial sums process, normalized by N1/αβ , weakly converges to an αβ-stable Lévy process, provided that the normalization dominates the corresponding k* th-order Hermite process normalization, or that 1/αβ> 1 - (2β-1)k*/2. A complete characterization of limit distributions of the partial sums process remains open.

Article information

Source
Bernoulli, Volume 10, Number 2 (2004), 327-355.

Dates
First available in Project Euclid: 19 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1082380222

Digital Object Identifier
doi:10.3150/bj/1082380222

Mathematical Reviews number (MathSciNet)
MR2046777

Zentralblatt MATH identifier
1076.62017

Keywords
Appell rank fractional derivative Hermite process long memory moving-average process partial sums process stable Lévy process

Citation

Surgailis, Donatas. Stable limits of sums of bounded functions of long-memory moving averages with finite variance. Bernoulli 10 (2004), no. 2, 327--355. doi:10.3150/bj/1082380222. https://projecteuclid.org/euclid.bj/1082380222


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