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Some comments on specification tests in nonparametric absolutely regular processes

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  • Dette, Holger
  • Spreckelsen, Ingrid

Abstract

In this note several aspects of specification tests in nonparametric models driven by an absolutely regular process are discussed, which were recently proprosed in the literature. In particular we give a more detailed asymptotic analysis of tests based on kernel methods under fixed alternatives using a central limit theorem for U-statistics with n-dependent nondegenerate kernel. As a by-product it is demonstrated that several results regarding the asymptotic distribution of goodness-of-fit tests are incorrectly stated in the literature. Moreover, our result indicates that recent results on the asymptotic equivalence between nonparametric autoregression and nonparametric regression cannot be used for the asymptotic analysis of goodness-of-fit tests under fixed alternatives.

Suggested Citation

  • Dette, Holger & Spreckelsen, Ingrid, 2001. "Some comments on specification tests in nonparametric absolutely regular processes," Technical Reports 2001,34, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200134
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    1. W. González-Manteiga & R. Cao, 1993. "Testing the hypothesis of a general linear model using nonparametric regression estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(1), pages 161-188, December.
    2. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    3. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    4. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
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