Using canonical correlations in testing for common nonlinear components

The paper discusses the use of canonical correlations for modelling multiple equation systems with common nonlinear components of a smooth transition type.The coefficients in a smooth transition regression model are assumed to be nonlinear continuous functions of a properly chosen transition variable. The obtained model thus captures structural changes in the relationship between the observed economic variables. With the help of the canonical correlations technique a simple test for testing for common nonlinear components helps us interpret the relationships between different economic variables and also simplifies the specification and estimation of the equationsystem, since in this case a reduction in the dimension of nonlinear components is possible. It was shown by Anderson and Vahid (1998) that the test for common nonlinearities is related to the test statistic for the overidentifying restrictions in the generalized method of moments framework and that both tests have the same asymptotic distribution. As an application of the described modelling approach, a three-variable linear vector autoregressive (VAR) model of the consumer price index for Slovenia and Austria and the nominal exchange rate between the currencies of both countriesis investigated. A single common nonlinear component is detected in all 3 equations and the estimated multivariate logistic smooth transition autoregressive model is discussed