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A Low-Dimension Portmanteau Test for Non-linearity

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  • Jennifer Castle
  • David Hendry

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-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.

Suggested Citation

  • Jennifer Castle & David Hendry, 2010. "A Low-Dimension Portmanteau Test for Non-linearity," Economics Series Working Papers 471, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:471
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    Cited by:

    1. Stillwagon, Josh R., 2016. "Non-linear exchange rate relationships: An automated model selection approach with indicator saturation," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 84-109.
    2. Anne Péguin-Feissolle & Bilel Sanhaji, 2016. "Tests of the Constancy of Conditional Correlations of Unknown Functional Form in Multivariate GARCH Models," Annals of Economics and Statistics, GENES, issue 123-124, pages 77-101.
    3. Francisco Salas-Molina & Juan A. Rodr'iguez-Aguilar & Joan Serr`a & Montserrat Guillen & Francisco J. Martin, 2016. "Empirical analysis of daily cash flow time series and its implications for forecasting," Papers 1611.04941, arXiv.org, revised Jun 2017.
    4. David F. Hendry, 2011. "Empirical Economic Model Discovery and Theory Evaluation," Rationality, Markets and Morals, Frankfurt School Verlag, Frankfurt School of Finance & Management, vol. 2(46), October.
    5. Hendry, David F., 2018. "Deciding between alternative approaches in macroeconomics," International Journal of Forecasting, Elsevier, vol. 34(1), pages 119-135.
    6. Castle Jennifer L. & Doornik Jurgen A & Hendry David F., 2011. "Evaluating Automatic Model Selection," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-33, February.
    7. Anne Péguin-Feissolle & Bilel Sanhaji, 2015. "Testing the Constancy of Conditional Correlations in Multivariate GARCH-type Models (Extended Version with Appendix)," Working Papers halshs-01133751, HAL.
    8. Holland, Marcio & Marçal, Emerson & de Prince, Diogo, 2020. "Is fiscal policy effective in Brazil? An empirical analysis," The Quarterly Review of Economics and Finance, Elsevier, vol. 75(C), pages 40-52.
    9. David F. Hendry & Grayham E. Mizon, 2016. "Improving the teaching of econometrics," Cogent Economics & Finance, Taylor & Francis Journals, vol. 4(1), pages 1170096-117, December.
    10. Frank Asche, Atle Oglend, and Petter Osmundsen, 2017. "Modeling UK Natural Gas Prices when Gas Prices Periodically Decouple from the Oil Price," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    11. Jennifer L. Castle & Jurgen A. Doornik & David F. Hendry, 2013. "Model Selection in Equations with Many ‘Small’ Effects," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(1), pages 6-22, February.
    12. Jurgen A. Doornik & David F. Hendry & Steve Cook, 2015. "Statistical model selection with “Big Data”," Cogent Economics & Finance, Taylor & Francis Journals, vol. 3(1), pages 1045216-104, December.
    13. Jurgen A. Doornik, 2016. "An Example of Instability: Discussion of the Paper by Søren Johansen and Bent Nielsen," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 357-359, June.
    14. Jennifer Castle & David Hendry, 2013. "Semi-automatic Non-linear Model selection," Economics Series Working Papers 654, University of Oxford, Department of Economics.
    15. David F. Hendry, 2020. "First in, First out: Econometric Modelling of UK Annual CO_2 Emissions, 1860–2017," Economics Papers 2020-W02, Economics Group, Nuffield College, University of Oxford.
    16. Josh R. Stillwagon, 2015. "TIPS and the VIX: Non-linear Spillovers from Financial Panic to Breakeven Inflation," Working Papers 1502, Trinity College, Department of Economics.
    17. Mahalia Jackman & Roland Craigwell & Michelle Doyle-Lowe, 2013. "Nonlinearity in the reaction of the foreign exchange market to interest rate differentials: evidence from a small open economy with a long-term peg," Applied Financial Economics, Taylor & Francis Journals, vol. 23(4), pages 287-296, February.
    18. Anders Bredahl Kock & Timo Teräsvirta, 2010. "Forecasting with nonlinear time series models," CREATES Research Papers 2010-01, Department of Economics and Business Economics, Aarhus University.
    19. Jennifer L. Castle & Jurgen A. Doornik & David F. Hendry, 2020. "Robust Discovery of Regression Models," Economics Papers 2020-W04, Economics Group, Nuffield College, University of Oxford.
    20. Barry Harrison & Winston Moore, 2012. "Stock Market Efficiency, Non-Linearity, Thin Trading and Asymmetric Information in MENA Stock Markets," Economic Issues Journal Articles, Economic Issues, vol. 17(1), pages 77-93, March.
    21. Jennifer Castle & David Hendry, 2010. "Automatic Selection for Non-linear Models," Economics Series Working Papers 473, University of Oxford, Department of Economics.
    22. Bendik P. Andersen & Petter E. de Lange, 2021. "Efficiency in the Atlantic salmon futures market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(6), pages 949-984, June.
    23. Shahid IQBAL & Maqbool H. SIAL, 2016. "Projections of Inflation Dynamics for Pakistan: GMDH Approach," Journal of Economics and Political Economy, KSP Journals, vol. 3(3), pages 536-559, September.
    24. Jahyun Koo & Ivan Paya & David A. Peel, 2012. "The Bank of Korea's nonlinear monetary policy rule," Applied Economics Letters, Taylor & Francis Journals, vol. 19(12), pages 1193-1202, August.
    25. Ericsson Neil R., 2016. "Testing for and estimating structural breaks and other nonlinearities in a dynamic monetary sector," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(4), pages 377-398, September.

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    More about this item

    Keywords

    Functional form; Portmanteau test; Non-linearity; Principal components; Collinearity;
    All these keywords.

    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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