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A low-dimension portmanteau test for non-linearity

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Abstract

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] and [Teräsvirta et al., 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 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.

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