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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Jana Jurečková,
  • Olcay Arslan,
  • Yeşim Güney,
  • Yetkin Tuaç,
  • Jan Picek,
  • Martin Schindler

摘要

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.