A Low-Dimension Portmanteau Test for Non-linearity

A new test for non-linearity in the conditional mean is proposed using functions of the principal components of regressors.  The test extends the non-linearity tests based on Kolmogorov-Gavor polynomials (Thursby and Schmidt, 1977, Tsay, 1986, and Terasvirta, Lin and Granger, 1993), but circumvents problems of high dimensionality, is equivariant to collinearity, and includes exponential functions, so is a portmanteau test with power against a wide range of possible alternatives.  A Monte Carlo analysis compared the performance of the test to the optimal infeasible test and to alternative tests.  The relative performance of the test is encouraging: the test has the appropriate size and has high power in many situations.