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.