Sufficient statistics associated with a two-state second-order Markov chain

Abstract

SUMMARY Statistical inference for binomial processes with second-order Markov dependence is worked out. Sufficient statistics for the 2 2 parameters associated with the process are found and their exact joint distribution is given in a closed form. An algorithm for finding the probability of k successes in n dependent trials is developed and a simple estimation procedure is suggested and applied to a meteorological time series.