Afrika Statistika

Extreme value theory for nonstationary random coefficients time series with regularly varying tails

Aliou Diop and Saliou Diouf

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Abstract

We consider a class of nonstationary time series defined by $Y_t = \mu_t + \sum^{\infty}_{k=0} C_{t, k^{\sigma} t-k^{\eta}t-k}$ where $\{\eta_t ; t \in \mathbb{Z}\}$ is sequence of iid random variables with regularly varying tail probabilities, $\sigma_t$ is a scale parameter and $\{C_{t,k.} t \in \mathbb{Z}, K > 0\}$ an infinite array of random variables identically distributed called weights. In this article, the extreme value theory of ${Y_t}$ is studied. Under mild conditions, convergence results for a point process based on the moving averages are proved.

Article information

Source
Afr. Stat., Volume 5, Number 1 (2010), 268-278.

Dates
First available in Project Euclid: 1 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.as/1388545349

Mathematical Reviews number (MathSciNet)
MR2920304

Zentralblatt MATH identifier
1266.62062

Subjects
Primary: 62G32: Statistics of extreme values; tail inference 62G30: Order statistics; empirical distribution functions 62F12: Asymptotic properties of estimators

Keywords
Mixing condition Poisson process Regular varying function Nonstationary process

Citation

Diop, Aliou; Diouf, Saliou. Extreme value theory for nonstationary random coefficients time series with regularly varying tails. Afr. Stat. 5 (2010), no. 1, 268--278. https://projecteuclid.org/euclid.as/1388545349


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