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On the distribution of the sample autocorrelation coefficients

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  • Kan, Raymond
  • Wang, Xiaolu

Abstract

Sample autocorrelation coefficients are widely used to test the randomness of a time series. Despite its unsatisfactory performance, the asymptotic normal distribution is often used to approximate the distribution of the sample autocorrelation coefficients. This is mainly due to the lack of an efficient approach in obtaining the exact distribution of sample autocorrelation coefficients. In this paper, we provide an efficient algorithm for evaluating the exact distribution of the sample autocorrelation coefficients. Under the multivariate elliptical distribution assumption, the exact distribution as well as exact moments and joint moments of sample autocorrelation coefficients are presented. In addition, the exact mean and variance of various autocorrelation-based tests are provided. Actual size properties of the Box-Pierce and Ljung-Box tests are investigated, and they are shown to be poor when the number of lags is moderately large relative to the sample size. Using the exact mean and variance of the Box-Pierce test statistic, we propose an adjusted Box-Pierce test that has a far superior size property than the traditional Box-Pierce and Ljung-Box tests.

Suggested Citation

  • Kan, Raymond & Wang, Xiaolu, 2010. "On the distribution of the sample autocorrelation coefficients," Journal of Econometrics, Elsevier, vol. 154(2), pages 101-121, February.
    • Handle: RePEc:eee:econom:v:154:y:2010:i:2:p:101-121
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    1. Jan R. Magnus, 1978. "The moments of products of quadratic forms in normal variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 32(4), pages 201-210, December.
    2. Ansley, Craig F. & Kohn, Robert & Shively, Thomas S., 1992. "Computing p-values for the generalized Durbin-Watson and other invariant test statistics," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 277-300.
    3. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    4. Kan, Raymond, 2008. "From moments of sum to moments of product," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 542-554, March.
    5. Dufour, Jean-Marie & Roy, Roch, 1985. "Some robust exact results on sample autocorrelations and tests of randomness," Journal of Econometrics, Elsevier, vol. 29(3), pages 257-273, September.
    6. Oliver D. Anderson, 1993. "Exact General‐Lag Serial Correlation Moments And Approximate Low‐Lag Partial Correlation Moments For Gaussian White Noise," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(6), pages 551-574, November.
    7. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
    8. repec:adr:anecst:y:1986:i:4:p:05 is not listed on IDEAS
    9. Ali, Mukhtar M, 1984. "Distributions of the Sample Autocorrelations When Observations Are from a Stationary Autoregressive-Moving-Average Process," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(3), pages 271-278, July.
    10. Richardson, Matthew & Smith, Tom, 1991. "Tests of Financial Models in the Presence of Overlapping Observations," The Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 227-254.
    11. Zeng-Hua Lu & Maxwell King, 2002. "Improving The Numerical Technique For Computing The Accumulated Distribution Of A Quadratic Form In Normal Variables," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 149-165.
    12. Jan R. Magnus, 1979. "The expectation of products of quadratic forms in normal variables: the practice," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 33(3), pages 131-136, September.
    13. Jan R. Magnus, 1986. "The Exact Moments of a Ratio of Quadratic Forms in Normal Variables," Annals of Economics and Statistics, GENES, issue 4, pages 95-109.
    14. Robert B. Davies, 1980. "The Distribution of a Linear Combination of χ2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 323-333, November.
    15. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
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    Cited by:

    1. Hammami, Yacine & Lindahl, Anna, 2014. "An intertemporal capital asset pricing model with bank credit growth as a state variable," Journal of Banking & Finance, Elsevier, vol. 39(C), pages 14-28.
    2. 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.
    3. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2015. "An investigation into multivariate variance ratio statistics and their application to stock market predictability," CeMMAP working papers 13/15, Institute for Fiscal Studies.
    4. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2015. "An investigation into Multivariate Variance Ratio Statistics and their application to Stock Market Predictability," Cambridge Working Papers in Economics 1552, Faculty of Economics, University of Cambridge.
    5. Kian-Ping Lim & Weiwei Luo & Jae H. Kim, 2013. "Are US stock index returns predictable? Evidence from automatic autocorrelation-based tests," Applied Economics, Taylor & Francis Journals, vol. 45(8), pages 953-962, March.

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