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

Jana Jurečková (), Olcay Arslan (), Yeşim Güney (), Yetkin Tuaç (), Jan Picek () and Martin Schindler ()
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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

Statistical Papers, 2025, vol. 66, issue 3, No 20, 18 pages

Abstract: 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.

Keywords: Autoregression rank scores; Hypothesis testing; Linear regression; Rank test; Regression rank scores (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01689-8

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