Threshold Effects in Multivariate Error Correction Models

Abstract

We propose a testing procedure for assessing the presence of threshold effects in nonstationary vector autoregressive models with or without cointegration. Our approach involves first testing whether the long-run impact matrix characterizing the VECM type representation of the VAR switches according to the magnitude of some threshold variable and is valid regardless of whether the system is purely I(1), I(1) with cointegration or stationary. Once the potential presence of threshold effects is established we subsequently evaluate the cointegrating properties of the system in each regime through a model selection based approach whose asymptotic and finite sample properties are also established. This subsequently allows us to introduce a novel non-linear permanent and transitory decomposition of the vector process of interest.