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Minimum distance lack-of-fit tests under long memory errors

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  • Hira Koul
  • Donatas Surgailis
  • Nao Mimoto

Abstract

This paper discusses some tests of lack-of-fit of a parametric regression model when errors form a long memory moving average process with the long memory parameter $$0>d>1/2$$ 0 > d > 1 / 2 , and when design is non-random and uniform on $$[0,1]$$ [ 0 , 1 ] . These tests are based on certain minimized distances between a nonparametric regression function estimator and the parametric model being fitted. The paper investigates the asymptotic null distribution of the proposed test statistics and of the corresponding minimum distance estimators under minimal conditions on the model being fitted. The limiting distribution of these statistics are Gaussian for $$0>d>1/4$$ 0 > d > 1 / 4 and non-Gaussian for $$1/4>d>1/2$$ 1 / 4 > d > 1 / 2 . We also discuss the consistency of these tests against a fixed alternative. A simulation study is included to assess the finite sample behavior of the proposed test. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Hira Koul & Donatas Surgailis & Nao Mimoto, 2015. "Minimum distance lack-of-fit tests under long memory errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(2), pages 119-143, February.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:2:p:119-143
    DOI: 10.1007/s00184-014-0492-x
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    References listed on IDEAS

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    1. Giraitis, Liudas & Koul, Hira L. & Surgailis, Donatas, 1996. "Asymptotic normality of regression estimators with long memory errors," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 317-335, September.
    2. Ignacio N. Lobato & Peter M. Robinson, 1998. "A Nonparametric Test for I(0)," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 475-495.
    3. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    4. Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2007. "Approximations and limit theory for quadratic forms of linear processes," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 71-95, January.
    5. Koul, Hira L. & Baillie, Richard T. & Surgailis, Donatas, 2004. "Regression Model Fitting With A Long Memory Covariate Process," Econometric Theory, Cambridge University Press, vol. 20(3), pages 485-512, June.
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    Cited by:

    1. Hira L. Koul & Fang Li, 2020. "Comparing two nonparametric regression curves in the presence of long memory in covariates and errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 499-517, May.

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    Keywords

    Moving average errors; Local Whittle;

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