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Nonparametric tests for serial independence in linear model against a possible autoregression of error terms

Author

Listed:
  • Jana Jurečková

    (The Czech Academy of Sciences)

  • Olcay Arslan

    (Ankara University)

  • Yeşim Güney

    (Ankara University)

  • Yetkin Tuaç

    (Ankara University)

  • Jan Picek

    (Technical University of Liberec)

  • Martin Schindler

    (Technical University of Liberec)

Abstract

When time series data follow a linear model, the innovations are often assumed to be serially independent. However, many time series also frequently display an autoregression of error terms. When testing a hypothesis on regression parameters, the tests can be distorted by a possible autoregression. Noting that we construct a class of non-parametric tests for the hypothesis of serial independence of error terms in the linear model against an alternative of linear autoregression. The main tool of the test criteria is the regression rank scores corresponding to the hypothetical model. The remarkable performance of the proposed tests is demonstrated by a simulation study and two real data examples.

Suggested Citation

  • Jana Jurečková & Olcay Arslan & Yeşim Güney & Yetkin Tuaç & Jan Picek & Martin Schindler, 2025. "Nonparametric tests for serial independence in linear model against a possible autoregression of error terms," Statistical Papers, Springer, vol. 66(3), pages 1-18, April.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:3:d:10.1007_s00362-025-01689-8
    DOI: 10.1007/s00362-025-01689-8
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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    7. 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.
    8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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