Extreme Value Theory for Univariate Stationary Processes

Abstract

Extreme value theory assumes that random variables are independent and identically distributed. This assumption cannot occur in time series analysis. In this paper, we investigate the extremal behavior of a stationary Gaussian autoregressive model. The Kolmogorov-Smirnov goodness of fit test shows that block maxima data converges in probability to a Gumbel distribution, so the introduction of dependence assumption doesn’t affect the extreme values distribution type.