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New Weighted Portmanteau Statistics for Time Series Goodness of Fit Testing


  • Thomas J. Fisher
  • Colin M. Gallagher


We exploit ideas from high-dimensional data analysis to derive new portmanteau tests that are based on the trace of the square of the m th order autocorrelation matrix. The resulting statistics are weighted sums of the squares of the sample autocorrelation coefficients that, unlike many other tests appearing in the literature, are numerically stable even when the number of lags considered is relatively close to the sample size. The statistics behave asymptotically as a linear combination of chi-squared random variables and their asymptotic distribution can be approximated by a gamma distribution. The proposed tests are modified to check for nonlinearity and to check the adequacy of a fitted nonlinear model. Simulation evidence indicates that the proposed goodness of fit tests tend to have higher power than other tests appearing in the literature, particularly in detecting long-memory nonlinear models. The efficacy of the proposed methods is demonstrated by investigating nonlinear effects in Apple, Inc., and Nikkei-300 daily returns during the 2006--2007 calendar years. The supplementary materials for this article are available online.

Suggested Citation

  • Thomas J. Fisher & Colin M. Gallagher, 2012. "New Weighted Portmanteau Statistics for Time Series Goodness of Fit Testing," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 777-787, June.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:777-787 DOI: 10.1080/01621459.2012.688465

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    References listed on IDEAS

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    5. Kasahara, Yukio & Pourahmadi, Mohsen & Inoue, Akihiko, 2009. "Duals of random vectors and processes with applications to prediction problems with missing values," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1637-1646, July.
    6. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
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    8. Hannan, E J & Terrell, R D & Tuckwell, N E, 1970. "The Seasonal Adjustment of Economic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(1), pages 24-52, February.
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    Cited by:

    1. Ke Zhu, 2016. "Bootstrapping the portmanteau tests in weak auto-regressive moving average models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 463-485, March.
    2. Butucea, Cristina & Zgheib, Rania, 2016. "Sharp minimax tests for large Toeplitz covariance matrices with repeated observations," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 164-176.
    3. Smith, Geoffrey Peter, 2016. "Weekday variation in the leverage effect: A puzzle," Finance Research Letters, Elsevier, vol. 17(C), pages 193-196.
    4. Colin M. Gallagher & Thomas J. Fisher, 2015. "On Weighted Portmanteau Tests For Time-Series Goodness-Of-Fit," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 67-83, January.
    5. Kokoszka, Piotr & Reimherr, Matthew & W├Âlfing, Nikolas, 2016. "A randomness test for functional panels," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 37-53.

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