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- Title
LIMIT THEOREMS FOR LONG-MEMORY STOCHASTIC VOLATILITY MODELS WITH INFINITE VARIANCE: PARTIAL SUMS AND SAMPLE COVARIANCES.
- Authors
KULIK, RAFAŁ; SOULIER, PHILIPPE
- 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.
- Subjects
LIMIT theorems; STOCHASTIC models; MARKET volatility; INFINITY (Mathematics); PARTIAL sums (Series); ANALYSIS of covariance; STOCHASTIC convergence
- Publication
Advances in Applied Probability, 2012, Vol 44, Issue 4, p1113
- ISSN
0001-8678
- Publication type
Article
- DOI
10.1239/aap/1354716591