Diagnostic check for heavy tail in linear time series

Justification of heavy tail is an important open problem. A systematic approach is proposed to verify heavy tail in linear time series. It consists of three parts, each of which is guided by statistical tests. The analysis is supplemented by an application to ozone concentration. The methodology has the advantage that the threshold selection is data-driven. Simulations show that test results are accurate even under model misspecification. The power is good under two heavy-tailed alternatives. The test is invariant when the time series clusters at extreme level in the study of the max-autoregressive process. It also gives a preliminary measure of tail heaviness if the underlying process is heavy-tailed.