Nonlinear cointegration with mixing errors

In this paper we consider an extension of the linear concept of co integration to a nonlinear context. We discuss the advantages and disadvantages of alternatives concepts of 1(0) and 1(1) based on the concept of a-mixing and study their relationship with the concept of short memory in distribution. Our concept of nonlinear co integration can be introduced without having to formally characterize the time series properties of the nonlinear transformations of 1(1) variables. The nonlinear least squares (NLS) estimator of the co integrating relationship is studied under alternative assumptions provided that the nonlinear function is Hadamard differentiable. With some Monte Carlo simulation we found that the bias of NLS estimator can either be large or small depending on the type of nonlinearity allowed in the individual series or in the co integrating function. We conclude that the proposed framework allows interesting extensions of the classical approach, but is not flexible enough to include several interesting nonlinearities.