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A. Kavkler, B. Böhm:
"Using Canonical Correlations in Testing for Common Nonlinear Components";
metodoloski zvezki (Advances in Methodology and Statistics), 3 (2006), 1; 75 - 88.

The paper discusses the use of canonical correlations for modeling
multiple equation systems with common nonlinear components of a
smooth transition type. The coefficients in a smooth transition re-
gression 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 to
interpret the relationships between different economic variables and
also simplifies the specification and estimation of the equation sys-
tem, since in this case reduction in the dimension of nonlinear com-
ponents 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 modelling approach described, 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 countries is investigated. A single common nonlinear component is detected in all 3 equations and the estimated nonlinear logistic vector smooth transition regression (LVSTR) model is discussed.

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