The present work focuses on the second order Markov chain model which arises in a variety of settings and is well-suited to be modeled in many applications. The efficiency of the maximum quasi-likelihood estimators with the full maximum likelihood estimators for second order Markov chain models are given, besides the limiting normality results on the asymptotic properties of the associated estimates. Some efficiency calculations are also given to discuss the feasibility and computational complexity of the QL approach relative to the full likelihood approach.
