TY - JOUR

T1 - A new look at portmanteau tests

AU - Akashi, Fumiya

AU - Odashima, Hiroaki

AU - Taniguchi, Masanobu

AU - Monti, Anna Clara

N1 - Funding Information:
The first and third author were supported by the JSPS Grant-in-Aid for Young Scientists (B): 16K16022 (Akashi, F., Waseda University) and JSPS Grant-in-Aid: 15H02061 (Taniguchi, M., Waseda University), respectively.
Publisher Copyright:
© 2017, Indian Statistical Institute.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Asymptotic local power

KW - Portmanteau test

KW - Serial correlation

KW - Time series analysis

KW - Variable selection

UR - http://www.scopus.com/inward/record.url?scp=85050491166&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050491166&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85050491166

SN - 0972-7671

VL - 80A

SP - 121

EP - 137

JO - Sankhya: The Indian Journal of Statistics

JF - Sankhya: The Indian Journal of Statistics

ER -