Abstract

In this article we show that the Hurst parameter and a well-known wavelet estimator fail to distinguish on/o models with substantially dierent distributions of on-times. We identify the problem as arising when standard power spectrum techniques, which are well-dened for commonly considered processes, are applied to processes with extremely heavy tailed on-times. We provide an elementary mechanism whereby such extremely heavy-tailed on-time processes arise in a simple queuing model.