On testing for nonlinearity in multivariate time series

This paper considers a multivariate extension of the test for neglected nonlinearity proposed by Tsay (1986) that uses principal components to overcome the problem of dimensionality that is common with tests of this type. Monte Carlo experiments reveal that the modified multivariate test provides a significant dimensional reduction without suffering from any systematic level distortion or power loss, and is more powerful than univariate nonlinearity tests.