Ambiguities in estimates of critical exponents for long-range dependent processes
Duffy, Ken and King, Christopher and Malone, David (2007) Ambiguities in estimates of critical exponents for long-range dependent processes. Physica A: Statistical Mechanics and its Applications , 377 (1). pp. 43-52. ISSN 0378-4371
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.
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