A note on tests for nonlinearity in a vector time series

A multivariate extension of the univariate nonlinearity test of Tsay (1986) is presented. Simulation results show that the multivariate test is more p owerful than its univariate counterpart, especially for series having nonli near structure involving several components of the vector process and weakl y or moderately cross-correlated process error terms. For illustration, the test is applied to a set of seasonally adjusted quarterly capital expendit ures and appropriations in U.S. manufacturing and a vector nonlinear model for the data is constructed.