Trimmed stable AR(1) processes

Alina Bazarova, István Berkes, Lajos Horvath

Research output: Contribution to journalArticlepeer-review


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)≥ (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 languageEnglish
Pages (from-to)3441-3462
JournalStochastic Processes and their Applications
Issue number10
Publication statusPublished - 2014


  • Trimming
  • Heavy tails
  • Asymptotic normality
  • Autoregressive(1) processes
  • CUSUM processes

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


Dive into the research topics of 'Trimmed stable AR(1) processes'. Together they form a unique fingerprint.

Cite this