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.
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Acknowledgements
Authors thank the Associate Editor and an anonymous Referee for their constructive comments on an earlier version of the paper. The third author thanks the Research Institute for Science & Engineering, Waseda University, for their supports.
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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.
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Akashi, F., Odashima, H., Taniguchi, M. et al. A New Look at Portmanteau Tests. Sankhya A 80, 121–137 (2018). https://doi.org/10.1007/s13171-017-0109-3
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DOI: https://doi.org/10.1007/s13171-017-0109-3