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The properties of some goodness-of-fit tests

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  • G. Boero
  • J. Smith
  • KF. Wallis

Abstract

The properties of Pearson's goodness-of-fit test, as used in density forecast evaluation, income distribution analysis and elsewhere, are analysed. The components-of-chi-squared or "Pearson analog" tests of Anderson (1994) are shown to be less generally applicable than was originally claimed. For the case of equiprobable classes, where the general components tests remain valid, a Monte Carlo study shows that tests directed towards skewness and kurtosis may have low power, due to differences between the class boundaries and the intersection points of the distributions being compared. The power of individual component tests can be increased by the use of nonequiprobable classes.

Suggested Citation

  • G. Boero & J. Smith & KF. Wallis, 2002. "The properties of some goodness-of-fit tests," Working Paper CRENoS 200209, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    • Handle: RePEc:cns:cnscwp:200209
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    1. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, "undated". "Evaluating Density Forecasts," CARESS Working Papres 97-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
    2. repec:sae:niesru:v:167:y::i:1:p:106-112 is not listed on IDEAS
    3. Wallis, Kenneth F., 2003. "Chi-squared tests of interval and density forecasts, and the Bank of England's fan charts," International Journal of Forecasting, Elsevier, vol. 19(2), pages 165-175.
    4. Engle, Robert F. & White (the late), Halbert (ed.), 1999. "Cointegration, Causality, and Forecasting: Festschrift in Honour of Clive W. J. Granger," OUP Catalogue, Oxford University Press, number 9780198296836.
    5. Boero, Gianna & Marrocu, Emanuela, 2002. "The Performance of Non-linear Exchange Rate Models: A Forecasting Comparison," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 21(7), pages 513-542, November.
    6. Arulampalam, W. & Robin A. Naylor & Jeremy P. Smith, 2002. "University of Warwick," Royal Economic Society Annual Conference 2002 9, Royal Economic Society.
    7. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
    8. Francis X. Diebold & Anthony S. Tay & Kenneth F. Wallis, 1997. "Evaluating Density Forecasts of Inflation: The Survey of Professional Forecasters," NBER Working Papers 6228, National Bureau of Economic Research, Inc.
    9. Gordon Anderson, 2001. "The Power And Size Of Nonparametric Tests For Common Distributional Characteristics," Econometric Reviews, Taylor & Francis Journals, vol. 20(1), pages 1-30.
    10. Kenneth F. Wallis, 1999. "Asymmetric density forecasts of inflation and the Bank of England's fan chart," National Institute Economic Review, National Institute of Economic and Social Research, vol. 167(1), pages 106-112, January.
    11. Anderson, Gordon, 1994. "Simple tests of distributional form," Journal of Econometrics, Elsevier, vol. 62(2), pages 265-276, June.
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    Cited by:

    1. Boero, Gianna & Smith, Jeremy & Wallis, Kenneth F., 2004. "Decompositions of Pearson's chi-squared test," Journal of Econometrics, Elsevier, vol. 123(1), pages 189-193, November.
    2. Boero, Gianna & Marrocu, Emanuela, 2004. "The performance of SETAR models: a regime conditional evaluation of point, interval and density forecasts," International Journal of Forecasting, Elsevier, vol. 20(2), pages 305-320.
    3. G. Marletto, 2006. "La politica dei trasporti come politica per l'innovazione: spunti da un approccio evolutivo," Working Paper CRENoS 200605, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    4. OA Carboni & G Medda, 2007. "Government Size and the Composition of Public Spending in a Neoclassical Growth Model," Working Paper CRENoS 200701, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.

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    More about this item

    Keywords

    nonequiprobable partitions; pearson's goodness-of-fit test; component tests; distributional assumptions; monte carlo; normality;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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