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Limit theorems for long-memory stochastic volatility models with infinite variance: partial sums and sample covariances. (English) Zbl 1275.62072
Authors’ abstract: We extend the existing literature on the asymptotic behavior of partial sums and 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.

##### MSC:
 62P05 Applications of statistics to actuarial sciences and financial mathematics 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60F05 Central limit and other weak theorems 62E20 Asymptotic distribution theory in statistics 60G70 Extreme value theory; extremal stochastic processes
##### Keywords:
heavy tails; long-range dependence; sample autocovariance
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