Testing Common Nonlinear Features in Nonlinear Vector Autoregressive Models

This paper studies a special class of vector smooth-transition autoregressive (VS- TAR) models containing common nonlinear features (CNFs). To test the existence of CNFs in a VSTAR model, a triangular representation for such a system containing CNFs is proposed. A procedure of testing CNFs in a VSTAR model is consisting of two steps: first, test unit root in a STAR model against a stable STAR process for each individual time series; secondly, examine if nonlinear features are common in the system by a La- grange Multiplier (LM) test when the null of unit root is rejected in the first step. The asymptotic distribution of the LM test is derived. Simulation studies of both unit root test and LM test have been carried out to investigate the finite sample properties. In the empirical application, the procedure of testing CNFs is illustrated by analyzing the monthly growth of consumption and income data of United States (1985:1 to 2011:11). The consumption and income system contains CNFs, and an estimated common nonlin- ear factor in VSTAR model is suggested.