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December 2012 Limit theorems for long-memory stochastic volatility models with infinite variance: partial sums and sample covariances
RAFAŁ KULIK, PHILIPPE SOULIER
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Adv. in Appl. Probab. 44(4): 1113-1141 (December 2012). DOI: 10.1239/aap/1354716591

Abstract

In this paper we extend the existing literature on the asymptotic behavior of the partial sums and the sample covariances of long-memory stochastic volatility models in the case of infinite variance. We also consider models with leverage, for which our results are entirely new in the infinite-variance case. Depending on the interplay between the tail behavior and the intensity of dependence, two types of convergence rates and limiting distributions can arise. In particular, we show that the asymptotic behavior of partial sums is the same for both long memory in stochastic volatility and models with leverage, whereas there is a crucial difference when sample covariances are considered.

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RAFAŁ KULIK. PHILIPPE SOULIER. "Limit theorems for long-memory stochastic volatility models with infinite variance: partial sums and sample covariances." Adv. in Appl. Probab. 44 (4) 1113 - 1141, December 2012. https://doi.org/10.1239/aap/1354716591

Information

Published: December 2012
First available in Project Euclid: 5 December 2012

zbMATH: 1275.62072
MathSciNet: MR3052851
Digital Object Identifier: 10.1239/aap/1354716591

Subjects:
Primary: 60G55
Secondary: 60F05, 62M10, 62P05

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 4 • December 2012
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