A new look at portmanteau tests

Fumiya Akashi, Hiroaki Odashima, Masanobu Taniguchi, Anna Clara Monti

Research output: Contribution to journalArticlepeer-review

Abstract

Portmanteau tests are some of the most commonly used statistical methods for model diagnostics. They can be applied in model checking either in the time series or in the regression context. The present paper proposes a portmanteau-type test, based on a sort of likelihood ratio statistic, useful to test general parametric hypotheses inherent to statistical models, which includes the classical portmanteau tests as special cases. Sufficient conditions for the statistic to be asymptotically chi-square distributed are elucidated in terms of the Fisher information matrix, and the results have very clear implications for the relationships between the parameter of interest and nuisance parameter. In addition, the power of the test is investigated when local alternative hypotheses are considered. Some interesting applications of the proposed test to various problems are illustrated, such as serial correlation tests where the proposed test is shown to be asymptotically equivalent to classical tests. Since portmanteau tests are widely used in many fields, it appears essential to elucidate the fundamental mechanism in a unified view.

Original languageEnglish
Pages (from-to)121-137
Number of pages17
JournalSankhya: The Indian Journal of Statistics
Volume80A
Publication statusPublished - 2018 Jan 1

Keywords

  • Asymptotic local power
  • Portmanteau test
  • Serial correlation
  • Time series analysis
  • Variable selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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