  We focus on the parametric estimation of the distribution of a Markov
environment from the observation of a single trajectory of a one-dimensional
nearest-neighbor path evolving in this random environment. In the ballistic
case, as the length of the path increases, we prove consistency, asymptotic
normality and efficiency of the maximum likelihood estimator. Our contribution
is two-fold: we cast the problem into the one of parameter estimation in a
hidden Markov model (HMM) and establish that the bivariate Markov chain
underlying this HMM is positive Harris recurrent. We provide different examples
of setups in which our results apply, in particular that of DNA unzipping
model, and we give a simple synthetic experiment to illustrate those results.
