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A Low-Dimension Collinearity-Robust Test for Non-linearity


  • Jennifer L. Castle
  • David F. Hendry


A new test for non-linearity is developed using weighted combinations of regressor powers based on the eigenvectors of the variance-covariance matrix. The test extends the ingenious test for heteroskedasticity proposed by White (1980), but both circumvents problems of high dimensionality and collinearity, and allows inclusion of cubic functions to ensure power against asymmetry or skewness. A Monte Carlo analysis compares the performance of the test to the optimal infeasible test and to a variant of White`s test. The relative performance of the test is encouraging: the test has the appropriate size and has high power in many situations. Furthermore, collinearity between regressors can increase the power of the test.

Suggested Citation

  • Jennifer L. Castle & David F. Hendry, 2007. "A Low-Dimension Collinearity-Robust Test for Non-linearity," Economics Series Working Papers 326, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:326

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    References listed on IDEAS

    1. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April.
    2. Quandt, Richard E., 1983. "Computational problems and methods," Handbook of Econometrics,in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 12, pages 699-764 Elsevier.
    3. Brock, W.A. & Dechert, W.D. & LeBaron, B. & Scheinkman, J.A., 1995. "A Test for Independence Based on the Correlation Dimension," Working papers 9520, Wisconsin Madison - Social Systems.
    4. Hendry, David F., 1995. "Dynamic Econometrics," OUP Catalogue, Oxford University Press, number 9780198283164.
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    Cited by:

    1. Castle, Jennifer L. & Hendry, David F., 2009. "The long-run determinants of UK wages, 1860-2004," Journal of Macroeconomics, Elsevier, vol. 31(1), pages 5-28, March.

    More about this item


    Functional Form Test; Non-linearity; Collinearity;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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