Testing for Nonlinearity in a Vector Time Series

We investigate tests to detect general nonlinear behavior in a vector time series. The proposed tests are multivariate extensions of the univariate nonlinearity tests of Keenan (1985) and Tsay (1986). Simulation results show that, in general, the multivariate tests are more powerful than their univariate counterparts, especially for series having nonlinear structure that involves several components of the vector process and process error terms that are weakly or moderately cross-correlated. For illustration, we apply the tests to several standard multivariate data sets. We then analyze a set of seasonally adjusted quarterly capital expenditures and appropriations in U.S. manufacturing over the period 1953 to 1974 in more detail, to illustrate how one might build a vector nonlinear model and the gains that may achieved from allowing for nonlinear behavior in a vector series. Some key words: Likelihood Ratio; Multivariate time series; Nonlinearity