Testing multiple equation systems for common nonlinear components

This paper provides a generalized method of moments test for common nonlinear components in multiple time series. The test statistic is presented in terms of the canonical correlations between the multiple series and a judicially chosen set of test regressors, and its performance in small samples is evaluated using Monte Carlo simulations. Two applications highlight the usefulness of this test in multivariate modelling. The first shows that the asymmetries which characterize the US and Canadian business cycles can be attributed to a common nonlinear factor, while the second shows that a single nonlinear factor can account for neglected nonlinearity in an empirical real business cycle model. Each of the implied nonlinear factor models shows potential for forecasting.