engleski

Anchoring the tail process

The tail process of a stationary time series, if it exists, describes the local behavior of the series around a typical exceedance over a large threshold. We intuitively explain that, for a large class of weakly dependent time series, the distribution of the tail process can be viewed as a length-biased version of the asymptotic distribution of a typical cluster of extremes. In order to obtain the latter distribution from the tail process, one needs to debias, and we formalize this idea by introducing the so-called concept of anchoring. We further exploit this relationship to give an another view on the properties of the tail process, such as the time-change formula. If time permits, we will discuss the so-called complete point process convergence result.

tail process ; stationarity

nije evidentirano