## Afrika Statistika

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

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

#### 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