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Limit Theorems for Long-Memory Stochastic Volatility Models with Infinite Variance: Partial Sums and Sample Covariances

Part of: Stochastic processes Limit theorems Inference from stochastic processes Applications

Published online by Cambridge University Press:  04 January 2016

Rafał Kulik  and
Philippe Soulier
Rafał Kulik*
Affiliation:
University of Ottawa
Philippe Soulier*
Affiliation:
Université Paris Ouest-Nanterre
*
∗ Postal address: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa ON, K1N 6N5, Canada. Email address: rkulik@uottawa.ca
∗∗ Postal address: Département de Mathématiques, Université Paris Ouest-Nanterre, 200 Avenue de la République, 92000 Nanterre Cedex, France. Email address: philippe.soulier@u-paris10.fr
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Abstract

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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.

Keywords

Heavy taillong-range dependencesample autocovariancestochastic volatility

MSC classification

Primary: 60G55: Point processes
Secondary: 60F05: Central limit and other weak theorems 62M10: Time series, auto-correlation, regression, etc. 62P05: Applications to actuarial sciences and financial mathematics
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 44 , Issue 4 , December 2012 , pp. 1113 - 1141
Copyright
© Applied Probability Trust 

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