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Nonlinear cointegration and nonlinear error correction

Santiago Mira and Alvaro Escribano ()

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: The relationships between stochastic trending variables given by the concepts of cointegration and error correction (EC) are well characterized in a linear context, but the extension to a nonlinear context is still a challenge. Few extensions of the linear framework were developed in the context of linear cointegration but nonlinear error correction (NEC) models, and even in this context, there are still many open questions. The theoretical framework is not well developed at this moment and only particular cases have been discussed empirically. In this paper we propose a statistical framework that allow us to address those issues. First, we generalize the notion of integration to the nonlinear case. As a result a generalization of cointegration is feasible, and also a formal definition of NEC models. Within this framework we analyze the nonlinear least squares (NLS) estimation of nonlinear cointegration relations and the extension of the two-step estimation procedures of Engle and Granger (1987) for NEC models. Finally, we discuss a generalization of Granger Representation Theorem to the nonlinear case and discuss the properties of the onestep (NLS) procedure to estimate NEC models.

Keywords: Nonlinear; cointegration; Nonlinear; error; correction; Mixing; Near; epoch; dependence; Long; memory; Granger; representatíon; theorem (search for similar items in EconPapers)
Date: 1996-07
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