A0253
Title: Asymptotics of sample tail autocorrelations for tail dependent time series: Phase transition and visualization
Authors: Ting Zhang - University of Georgia (United States) [presenting]
Abstract: An asymptotic theory on sample tail autocorrelations of time series data is developed that can exhibit serial dependence in both tail and non-tail regions. Unlike the traditional autocorrelation function, the study of tail autocorrelations requires a double asymptotic scheme to capture the tail phenomena, and the results do not impose any restriction on the dependence structure in non-tail regions and allow processes that are not necessarily strong mixing. The asymptotic theory indicates a phase transition phenomenon for sample tail autocorrelations, whose asymptotic behavior, including the convergence rate, can transit from one phase to the other when the lag index moves past the point beyond which serial tail dependence vanishes. The phase transition fills the gap of existing research on tail autocorrelations and can be used to construct the lines of significance, in analogy to the traditional autocorrelation plot, when visualizing sample tail autocorrelations to assess the existence of serial tail dependence or to identify the maximal lag of tail dependence.
