Abstract
Hidden semi-Markov models have been proposed in Meier-Hellstern et al (1991) to model the times between transmission of packets at a source. In this paper, we specifically investigate such models where the distributions associated with one or more of the states are heavy-tailed. We study the asymptotic properties of the sample covariance and correlation functions and show that the correlation function at nonzero lags is asymptotically equal to zero. Behavior of the sample autocorrelation function (acf) for a simulated five state semi-Markov model is contrasted with the behavior of the sample acf for a real data set in order to infer that the real data cannot be modeled by a hidden semi-Markov scheme
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