This paper describes a data reduction technique in case of a markov chain of specified order. Instead of observing all the transitions in a markov chain we record only a few of them and treat the remaining part as missing. The decision about which transitions to be filtered is taken before the observation process starts. Based on the filtered chain we try to estimate the parameters of the markov model using EM algorithm. In the first half of the paper we characterize a class of filtering mechanism for which all the parameters remain identifiable. In the later half we explain methods of estimation and testing about the transition probabilities of the markov chain based on the filtered data. The methods are first developed assuming a simple markov model with each probability of transition positive, but then generalized for models with structural zeroes in the transition probability matrix. Further extension is also done for multiple markov chains. The performance of the developed method of estimation is studied using simulated data along with a real life data.
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