Likelihood-based inference for cointegration with nonlinear error-correction

TY - JOUR

T1 - Likelihood-based inference for cointegration with nonlinear error-correction

AU - Kristensen, Dennis

AU - Rahbek, Anders Christian

PY - 2010/9

Y1 - 2010/9

N2 - 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.

AB - 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.

U2 - 10.1016/j.jeconom.2010.03.010

DO - 10.1016/j.jeconom.2010.03.010

M3 - Journal article

SN - 0304-4076

VL - 158

SP - 78

EP - 94

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 1

ER -