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Some comments on specification tests in nonparametric absolutely regular processes


  • Holger Dette
  • Ingrid Spreckelsen


In this note, several aspects of a recently proposed specification test in nonparametric models driven by an absolutely regular process are discussed. 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 or goodness-of-fit tests are incorrectly stated in the literature. Our result also indicates that results on the asymptotic equivalence of nonparametric autoregression and nonparametric regression cannot be used for the asymptotic analysis of goodness-of-fit tests under fixed alternatives. Copyright 2004 Blackwell Publishing Ltd.

Suggested Citation

  • Holger Dette & Ingrid Spreckelsen, 2004. "Some comments on specification tests in nonparametric absolutely regular processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 159-172, March.
  • Handle: RePEc:bla:jtsera:v:25:y:2004:i:2:p:159-172

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    References listed on IDEAS

    1. Paparoditis, Efstathios & Politis, Dimitris N, 2001. "Unit Root Testing via the Continuous-Path Block Bootstrap," University of California at San Diego, Economics Working Paper Series qt9qb4r775, Department of Economics, UC San Diego.
    2. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    3. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(02), pages 469-490, April.
    4. Anders Rygh Swensen, 2003. "Bootstrapping unit root tests for integrated processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 99-126, January.
    5. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, May.
    6. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    7. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    8. Swensen, Anders Rygh, 2003. "A Note On The Power Of Bootstrap Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(01), pages 32-48, February.
    9. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
    10. Parker, Cameron & Paparoditis, Efstathios & Politis, Dimitris N., 2006. "Unit root testing via the stationary bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 601-638, August.
    11. Paparoditis, Efstathios & Politis, Dimitris N., 2005. "Bootstrapping Unit Root Tests for Autoregressive Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 545-553, June.
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    Cited by:

    1. Dette, Holger & Wieczorek, Gabriele, 2007. "Testing for a constant coefficient of variation in nonparametric regression," Technical Reports 2007,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Holger Dette & Juan Carlos Pardo-Fernández & Ingrid Van Keilegom, 2009. "Goodness-of-Fit Tests for Multiplicative Models with Dependent Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 782-799.
    3. Amaro de Matos, Joao & Fernandes, Marcelo, 2007. "Testing the Markov property with high frequency data," Journal of Econometrics, Elsevier, vol. 141(1), pages 44-64, November.
    4. repec:wyi:journl:002114 is not listed on IDEAS
    5. Cai, Zongwu & Xiao, Zhijie, 2012. "Semiparametric quantile regression estimation in dynamic models with partially varying coefficients," Journal of Econometrics, Elsevier, vol. 167(2), pages 413-425.
    6. Dette, Holger & Weißbach, Rafael, 2009. "A bootstrap test for the comparison of nonlinear time series," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1339-1349, February.
    7. Dette, Holger & Pardo-Fernandez, Juan Carlos & van Keilegom, Ingrid, 2007. "Goodness-of-fit tests for multiplicativemodels with dependent data," Technical Reports 2007,34, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    8. Dette, Holger & Weißbach, Rafael, 2006. "A Bootstrap Test for the Comparison of Nonlinear Time Series - with Application to Interest Rate Modelling," Technical Reports 2006,30, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    9. Gao, Jiti & Gijbels, Irene, 2005. "Bandwidth selection for nonparametric kernel testing," MPRA Paper 11982, University Library of Munich, Germany, revised Jun 2007.
    10. Xu Guo & Wangli Xu & Lixing Zhu, 2015. "Model checking for parametric regressions with response missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 229-259, April.
    11. Yan-Yu Chiou & Mei-Yuan Chen & Jau-er Chen, 2017. "Nonparametric Regression with Multiple Thresholds: Estimation and Inference," Papers 1705.09418,, revised Feb 2018.

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