Raftery (1985) proposed a higher order Markov model that is parsimonious in terms of number of parameters. The model appears to be useful in many real life situations. However, many important properties of the model have not been investigated. In particular, estimation methods under various sampling situations have not been studied. In this paper the relative merits of the maximum likelihood and the minimum chi-square estimators for a single realization are considered. For other sampling situations, a nonlinear least squares estimator is proposed when only macro data are available. Its small sample properties are studied by simulation. An empirical Bayes estimator for panel data is also considered.