Trimmed stable AR(1) processes

Alina Bazarova; István Berkes; Lajos Horvath

doi:dx.doi,org/10.1016/j.spa.2014.05.001

Trimmed stable AR(1) processes

Alina Bazarova, István Berkes, Lajos Horvath

Institute of Statistics (5060)

Research output: Contribution to journal › Article › peer-review

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), 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
Pages (from-to)	3441-3462
Journal	Stochastic Processes and their Applications
Volume	124
Issue number	10
DOIs	https://doi.org/dx.doi,org/10.1016/j.spa.2014.05.001
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)

Access to Document

dx.doi,org/10.1016/j.spa.2014.05.001

Bazarova_Berkes_Horvath_Trimmed_stable_AR(1)-processes_StochasticProcesses_Appl_2014.pdfSubmitted manuscript, 418 KB
1-s2.0-S0304414914001112-mainAccepted author manuscript, 260 KB

Cite this

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title = "Trimmed stable AR(1) processes",

abstract = "In this paper we investigate the distribution of trimmed sums of dependentobservations with heavy tails. We consider the case of autoregressive processes of order onewith independent innovations in the domain of attraction of a stable law. We show if the dlargest (in magnitude) terms are removed from the sample, then the sum of the remainingelements satisfies a functional central limit theorem with random centering provided d =d(n) ≥ nγ (for some γ > 0), d(n)/n → 0. This result is used to get asymptotics for thewidely used CUSUM process in case of dependent heavy tailed observations",

keywords = "Trimming, Heavy tails, Asymptotic normality, Autoregressive(1) processes, CUSUM processes",

author = "Alina Bazarova and Istv{\'a}n Berkes and Lajos Horvath",

year = "2014",

doi = "dx.doi,org/10.1016/j.spa.2014.05.001",

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pages = "3441--3462",

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T1 - Trimmed stable AR(1) processes

AU - Bazarova, Alina

AU - Berkes, István

AU - Horvath, Lajos

PY - 2014

Y1 - 2014

N2 - In this paper we investigate the distribution of trimmed sums of dependentobservations with heavy tails. We consider the case of autoregressive processes of order onewith independent innovations in the domain of attraction of a stable law. We show if the dlargest (in magnitude) terms are removed from the sample, then the sum of the remainingelements satisfies a functional central limit theorem with random centering provided d =d(n) ≥ nγ (for some γ > 0), d(n)/n → 0. This result is used to get asymptotics for thewidely used CUSUM process in case of dependent heavy tailed observations

AB - In this paper we investigate the distribution of trimmed sums of dependentobservations with heavy tails. We consider the case of autoregressive processes of order onewith independent innovations in the domain of attraction of a stable law. We show if the dlargest (in magnitude) terms are removed from the sample, then the sum of the remainingelements satisfies a functional central limit theorem with random centering provided d =d(n) ≥ nγ (for some γ > 0), d(n)/n → 0. This result is used to get asymptotics for thewidely used CUSUM process in case of dependent heavy tailed observations

KW - Trimming

KW - Heavy tails

KW - Asymptotic normality

KW - Autoregressive(1) processes

KW - CUSUM processes

UR - http://www.sciencedirect.com/science/journal/aip/03044149

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U2 - dx.doi,org/10.1016/j.spa.2014.05.001

DO - dx.doi,org/10.1016/j.spa.2014.05.001

M3 - Article

VL - 124

SP - 3441

EP - 3462

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 10

ER -

Trimmed stable AR(1) processes

Abstract

Keywords

Fields of Expertise

Treatment code (Nähere Zuordnung)

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Asymptotic and Statistical Analysis of Time Series in Economy and Finance

Cite this

Trimmed stable AR(1) processes

Abstract

Keywords

Fields of Expertise

Treatment code (Nähere Zuordnung)

Access to Document

Other files and links

Fingerprint

Projects

Asymptotic and Statistical Analysis of Time Series in Economy and Finance

Cite this