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Nonparametric tests in linear model with autoregressive errors

Author

Listed:
  • Jana Jurečková

    (Academy of Sciences and Charles University)

  • Olcay Arslan

    (University of Ankara)

  • Yeşim Güney

    (University of Ankara)

  • Jan Picek

    (Technical University of Liberec)

  • Martin Schindler

    (Technical University of Liberec)

  • Yetkin Tuaç

    (University of Ankara)

Abstract

In the linear regression model with possibly autoregressive errors, we construct a family of nonparametric tests for significance of regression, under a nuisance autoregression of model errors. The tests avoid an estimation of nuisance parameters, in contrast to the tests proposed in the literature. A simulation study illustrate their good performance.

Suggested Citation

  • Jana Jurečková & Olcay Arslan & Yeşim Güney & Jan Picek & Martin Schindler & Yetkin Tuaç, 2023. "Nonparametric tests in linear model with autoregressive errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(4), pages 443-453, May.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:4:d:10.1007_s00184-022-00877-y
    DOI: 10.1007/s00184-022-00877-y
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    References listed on IDEAS

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    1. Koenker, Roger & Xiao, Zhijie, 2006. "Quantile Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 980-990, September.
    2. Marc Hallin & Jana Jureckova & Jan Picek & Toufik Zahaf, 1999. "Nonparametric tests of independence between two autoregressive series based on autoregression rank scores," ULB Institutional Repository 2013/2081, ULB -- Universite Libre de Bruxelles.
    3. Marc Hallin & Jana Jureckova, 1999. "Optimal tests for autoregressive models based on autoregression rank scores," ULB Institutional Repository 2013/2089, ULB -- Universite Libre de Bruxelles.
    4. Roger Koenker & Zhijie Xiao, 2004. "Unit Root Quantile Autoregression Inference," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 775-787, January.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. Marc Hallin & Jana Jureckova & Jan Picek & Toufik Zahaf, 1999. "Nonparametric tests of independence of two autoregressive time series based on autoregression rank scores," ULB Institutional Repository 2013/127942, ULB -- Universite Libre de Bruxelles.
    7. Marc Hallin & Faouzi El Bantli, 2001. "Kolmogorov-Smirnov tests for AR models based on autoregression rank scores," ULB Institutional Repository 2013/2161, ULB -- Universite Libre de Bruxelles.
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