Likelihood-based inference for cointegration with nonlinear error-correction

Abstract

We consider a class of nonlinear vector error correction models where the transfer function (or loadings) of the stationary relationships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties of the process in terms of stochastic and deterministic trends as well as stationary components. In particular, the behavior of the cointegrating relations is described in terms of geometric ergodicity. Despite the fact that no deterministic terms are included, the process will have both stochastic trends and a linear trend in general. Gaussian likelihood-based estimators are considered for the long-run cointegration parameters, and the short-run parameters. Asymptotic theory is provided for these and it is discussed to what extend asymptotic normality and mixed normality can be found. A simulation study reveals that cointegration vectors and the shape of the adjustment are quite accurately estimated by maximum likelihood. At the same time, there is very little information in data about some of the individual parameters entering the adjustment function if care is not taken in choosing a suitable specification.