Nonlinear error correction models

The relationship between co integration an error correction models (EC) is well characterized in a linear context, see Engle and Granger (1987) and Johansen (1991), but the extension to the nonlinear context is still a challenge. Few extensions of the linear framework were done in the context of nonlinear error correction (NEC), see Escribano (1986 and 1987), or asymmetric and time varying error correction models, see Granger and Lee (1989) and Burguess (1992). In this paper we propose a theoretical framework based on the concept of near epoch dependece (NED) that allow us to formally address those issues. In particular, we partially extend Granger Representation Theorem to the nonlinear case and we study the estimation and -inference properties of least squares when the co integrating relation is linear but the dynamic model is a NEC. The two-step estimation approach of Engle and Granger (1987) is extended when the co integrating errors are NED and the dynamic model is a NEC. Some potentially useful NEC models are proposed and Monte Carlo simulations are provided