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Abstract
In this paper we investigate the
distribution of trimmed sums of dependent observations with heavy tails.
We consider the case of autoregressive processes of order one with
independent innovations in the domain of attraction of a stable law. We
show if the d largest (in magnitude) terms are removed from the sample,
then the sum of the remaining elements satisfies a functional central
limit theorem with random centering provided d=d(n)≥nγ (for
some γ>0) and d(n)/n→0. This result is used to get asymptotics for
the widely used CUSUM process in case of dependent heavy tailed
observations.
Original language | English |
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Pages (from-to) | 3441-3462 |
Journal | Stochastic Processes and their Applications |
Volume | 124 |
Issue number | 10 |
DOIs | |
Publication status | Published - 2014 |
Keywords
- Trimming
- Heavy tails
- Asymptotic normality
- Autoregressive(1) processes
- CUSUM processes
Fields of Expertise
- Information, Communication & Computing
Treatment code (Nähere Zuordnung)
- Basic - Fundamental (Grundlagenforschung)
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Asymptotic and Statistical Analysis of Time Series in Economy and Finance
Hörmann, S., Schauer, J., Berkes, I. & Jirak, J. M.
1/01/02 → …
Project: Research area