We decompose a stationary Markov process (X^t) as: X^t = a^o + [Sommation from j=1 to infinity) a^j Z^(j,t), where the Z^j 's processes admit ARMA specifications. These decompositions are deduced from a nonlinear canonical decomposition of the joint distribution of (X^t, X^(t-1)).

Methods, like Maximum Empirical Likelihood (MEL), that operate within the Empirical Estimating Equations (E3) approach to estimation and inference are challenged by the Empty Set Problem (ESP). We propose to return from E3 back to the Estimating Equations, and to use the Maximum Likelihood...