A low-dimension portmanteau test for non-linearity

摘要

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-Gabor polynomials (Thursby and Schmidt, 1977;Tsay, 1986;Terasvirtaetal., 1993), but circumvents problems of high dimensionality, is equivariantto collinearity, and includes exponential functions, so is a portmanteau test with power against a wide range of possible alternatives. A Monte Carlo analysis compares 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.