Key points are not available for this paper at this time.
Adrian Raftery, Simon Tavare, Estimation and Modelling Repeated Patterns in High Order Markov Chains with the Mixture Transition Distribution Model, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 43, No. 1 (1994), pp. 179-199
Raftery et al. (Sat,) studied this question.