Stable limits for sums of dependent infinite variance random variables
By K. Bartkiewicz, Adam Jakubowski, Thomas Mikosch, Olivier Wintenberger. 2009
78 citations recorded by the source corpus.
The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to hold are known in the literature. However, most of these results are qualitative in the sense that the parameters of the limit distribution are expressed in terms of some limiting point process. In this paper we will be able to determine the parameters of the limiting stable distribution in terms of some tail characteristics of the underlying stationary sequence. We will apply our results to some standard time series models, including the GARCH(1, 1) process and its squares, the stochastic volatility models and solutions to stochastic recurrence equations.
View Paper: https://www.semanticscholar.org/paper/c7a57c597c1c5ab81e099933181b22755ae59939
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- Johan Segers
- Danijel Krizmani'c
- Bojan Basrak
- Richard A. Davis
- Thomas Mikosch
- Zenghu Li
- Henrik Hult
- Raphaël Huser
Citations in the corpus
- A functional limit theorem for dependent sequences with infinite variance stable limits (2010, background): “[3], providing a detailed study of the conditions for the convergence of the partial sums of a strictly stationary process to an infinite variance stable distribution.”