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

Published online by Cambridge University Press:  04 January 2016

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: [email protected]
∗∗ Postal address: Département de Mathématiques, Université Paris Ouest-Nanterre, 200 Avenue de la République, 92000 Nanterre Cedex, France. Email address: [email protected]
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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.

Type
General Applied Probability
Copyright
© Applied Probability Trust 

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