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Biometrika 1999 86(3):728-734; doi:10.1093/biomet/86.3.728
© 1999 by Biometrika Trust
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Miscellanea. A note on tests for nonlinearity in a vector time series

JL HarvillA1 and BK RayA2

A1 Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762, USA E-mail: harvill@math.msstate.edu A2 Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA E-mail: borayx@m.njit.edu

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

Key Words: Likelihood ratio; Multivariate time series; Nonlinear time series


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