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A New Look at Portmanteau Tests

Author

Listed:
  • Fumiya Akashi

    (Waseda University)

  • Hiroaki Odashima

    (Waseda University)

  • Masanobu Taniguchi

    (Waseda University)

  • Anna Clara Monti

    (University of Sannio)

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.

Suggested Citation

  • Fumiya Akashi & Hiroaki Odashima & Masanobu Taniguchi & Anna Clara Monti, 2018. "A New Look at Portmanteau Tests," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 121-137, February.
    • Handle: RePEc:spr:sankha:v:80:y:2018:i:1:d:10.1007_s13171-017-0109-3
    DOI: 10.1007/s13171-017-0109-3
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    References listed on IDEAS

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    1. Breusch, T S, 1978. "Testing for Autocorrelation in Dynamic Linear Models," Australian Economic Papers, Wiley Blackwell, vol. 17(31), pages 334-355, December.
    2. A. I. McLeod & W. K. Li, 1983. "Diagnostic Checking Arma Time Series Models Using Squared‐Residual Autocorrelations," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 269-273, July.
    3. Ngai Hang Chan & Lanh Tat Tran, 1992. "Nonparametric Tests For Serial Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(1), pages 19-28, January.
    4. Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-421, May.
    5. Godfrey, L G, 1976. "Testing for Serial Correlation in Dynamic Simultaneous Equation Models," Econometrica, Econometric Society, vol. 44(5), pages 1077-1084, September.
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    Cited by:

    1. Roberto Baragona & Francesco Battaglia & Domenico Cucina, 2022. "Data-driven portmanteau tests for time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 675-698, September.
    2. Tucker S. McElroy & Anindya Roy, 2022. "Model identification via total Frobenius norm of multivariate spectra," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 473-495, April.

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