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April 2004 Stable limits of sums of bounded functions of long-memory moving averages with finite variance
Donatas Surgailis
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Bernoulli 10(2): 327-355 (April 2004). DOI: 10.3150/bj/1082380222

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.

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Donatas Surgailis. "Stable limits of sums of bounded functions of long-memory moving averages with finite variance." Bernoulli 10 (2) 327 - 355, April 2004. https://doi.org/10.3150/bj/1082380222

Information

Published: April 2004
First available in Project Euclid: 19 April 2004

zbMATH: 1076.62017
MathSciNet: MR2046777
Digital Object Identifier: 10.3150/bj/1082380222

Rights: Copyright © 2004 Bernoulli Society for Mathematical Statistics and Probability

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Vol.10 • No. 2 • April 2004
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