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A Powerful Portmanteau Test of Lack of Fit for Time Series

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Abstract

A new portmanteau test for time series more powerful than the tests ofLjung and Box (1978) and Monti (1994} is proposed. The test is based on the pth root of the determinant of the pth autocorrelation matrix. It is shown that this statistic can be interpreted as the geometric mean of the squared multiple correlation coefficients with m lag values when m goes from 1 to p. It can also be interpreted as a geometric mean of the partial autocorrelation coefficients. The asymptotic distribution of the test statistic is obtained. This distribution is a linear combination of chi-squared distributions and it is shown that it can be approximated by a gamma distribution. The power of the test is compared with that of the Ljung and Box and Monti tests and it is shown that the proposed test can be up to 50% more powerful depending upon the model and sample size. The test is applied to the detection of nonlinearity by using the same matrix but with coefficients that are now the autocorrelations of the squared residuals. The new test is more powerful than the test of McLeod and Li (1983) for nonlinearity. An example is presented in which this test detects nonlinearity in the residuals of the sunpot series.
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  • Pena D. & Rodriguez J., 2002. "A Powerful Portmanteau Test of Lack of Fit for Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 601-610, June.
    • Handle: RePEc:bes:jnlasa:v:97:y:2002:m:june:p:601-610
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    1. 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.
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    3. Scott D. Watkins & Patrick L. Anderson, 2007. "Introduction," Palgrave Macmillan Books, in: Scott D. Watkins & Patrick L. Anderson (ed.), The State Economic Handbook 2008 Edition, pages 1-3, Palgrave Macmillan.
    4. Santiago Velilla, 1994. "A Goodness‐Of‐Fit Test For Autoregressive Moving‐Average Models Based On The Standardized Sample Spectral Distribution Of The Residuals," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(6), pages 637-647, November.
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    14. Serttas, Fatma Ozgu, 2010. "Essays on infinite-variance stable errors and robust estimation procedures," ISU General Staff Papers 201001010800002742, Iowa State University, Department of Economics.
    15. Bouhaddioui, Chafik & Ghoudi, Kilani, 2012. "Empirical processes for infinite variance autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 319-335.
    16. Kwan, Andy C.C. & Sim, Ah-Boon & Wu, Yangru, 2005. "A comparative study of the finite-sample performance of some portmanteau tests for randomness of a time series," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 391-413, February.
    17. 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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