In this paper we consider the problem of estimating the parameters of a Markov model using so-called macro data. It will be shown that the stochastic process of the macro data is a Markov chain, which uniquely determines the probability structure of the underlying Markov model. A conditional least squares estimator exists under very weak conditions and this estimator is strongly consistent as time tends to infinity. Moreover this estimator is shown to be asymptotically normal under some additional assumptions.
"On the Estimation of the Parameters of Markov Probability Models Using Macro Data." Ann. Statist. 11 (1) 78 - 85, March, 1983. https://doi.org/10.1214/aos/1176346058