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...

The paper presents a study of dependencies between the autocorrelation function and selected nonlinear transformations of time series. We examine parametric transformations and introduce an analysis of nonlinear canonical correlations. We also propose various methods of testing the...

In order to obtain exact distributional results without imposing restrictive parametric assumptions, various rank counterparts of the Dickey-Fuller statistic are considered. In particular, a rank counterpart of the score statistic is suggested which appears to have attractive theoretical...