A New Look at Portmanteau Tests

Fumiya Akashi (), Hiroaki Odashima (), Masanobu Taniguchi () and Anna Clara Monti ()
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Fumiya Akashi: Waseda University
Hiroaki Odashima: Waseda University
Masanobu Taniguchi: Waseda University
Anna Clara Monti: University of Sannio

Sankhya A: The Indian Journal of Statistics, 2018, vol. 80, issue 1, No 6, 137 pages

Abstract: 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.

Keywords: Portmanteau test; Asymptotic local power; Serial correlation; Time series analysis; Variable selection; 62F03; 62F05 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s13171-017-0109-3

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