A note on generalizing the concept of cointegration

Building on the time-varying-coefficient (TVC) model, we propose a generalization of the concept of cointegration, allowing for the possibility that a set of variables measured with error entails a nonlinear relationship with unknown functional form. Both the dependent and explanatory variables of this relationship may be nonstationary (not necessarily of unit-root type), but there exists a nonlinear combination of all these explanatory variables that completely explains all the variation in the dependent variable. The TVC model allows us to test for the presence of this generalized cointegration in the absence of knowledge of the true nonlinear functional form and the full set of explanatory variables. We present the basic stages of the technique and discuss in detail how the issues of nonstationarity and cointegration affect each stage of the TVC estimation procedure.