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

Jurečková J., Arslan O., Güney Y., Tuaç Y., Picek J., Schindler M.

STATISTICAL PAPERS, vol.66, no.3, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 66 Issue: 3
  • Publication Date: 2025
  • Doi Number: 10.1007/s00362-025-01689-8
  • Journal Name: STATISTICAL PAPERS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, IBZ Online, International Bibliography of Social Sciences, ABI/INFORM, Aerospace Database, Business Source Elite, Business Source Premier, Communication Abstracts, EconLit, zbMATH
  • Ankara University Affiliated: Yes

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.