Introducing Non-Linearity Into Cointegration

Abstract

A wide class of processes is considered in which initially a persistent series and a transient series are generated separately, as unobserved components, and from them a pair of observable series are generated as a weighted combination of the components. It follows that the observable series will be persistent but have a linear combination that is transient, aud so can be considered cointegrated. From the construction, the series need not be I(1) and other linear aspects of standard theory is removable, but often error-correction models are available. Some theoretical examples are provided.