Parameter estimation for Markov modulated poisson processes

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Abstract
A Markov modulated Poisson process (MMPP) is a doubly stochastic Poisson process whose intensity is controlled by a finite state continuous-time Markov chain. MMPPs have during the last decade been used to model traffic flows in communication networks as well as environmental data. We give a brief survey of methods, most of which are based on moment matching, that have earlier been proposed for estimating the parameters of MMPPs. Then we turn to likelihood based methods, prove a strong consistency property of the maximum likelihood estimator, and discuss some practical methods for calculating MLEs for two-state MMPPs