On the distribution of the sample autocorrelation coefficients
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.
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- 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.
- Dufour, J.M. & Roy, R., 1984. "Some Robust Exact Results on Sample Autocorrelations and Tests of Randomness," Cahiers de recherche 8412, Universite de Montreal, Departement de sciences economiques.
- Magnus, J.R., 1978. "The moments of products of quadratic forms in normal variables," Other publications TiSEM 17c77a44-1789-4cf4-a382-a, Tilburg University, School of Economics and Management.
- 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.
- James M. Poterba & Lawrence H. Summers, 1987. "Mean Reversion in Stock Prices: Evidence and Implications," NBER Working Papers 2343, National Bureau of Economic Research, Inc.
- 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.
- Andrew W. Lo, A. Craig MacKinlay, 1988.
"Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test,"
Review of Financial Studies,
Society for Financial Studies, vol. 1(1), pages 41-66.
- Tom Doan, . "VRATIO: RATS procedure to implement variance ratio unit root test procedure," Statistical Software Components RTS00231, Boston College Department of Economics.
- Andrew W. Lo & A. Craig MacKinlay, 1987. "Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test," NBER Working Papers 2168, National Bureau of Economic Research, Inc.
- 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.
- Magnus, J.R., 1986. "The exact moments of a ratio of quadratic forms in normal variables," Other publications TiSEM c6725407-ac3c-44fd-b6d1-5, Tilburg University, School of Economics and Management.
- 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 271-78, July.
- 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.
- Richardson, Matthew & Smith, Tom, 1991. "Tests of Financial Models in the Presence of Overlapping Observations," Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 227-54.
- Kan, Raymond, 2008. "From moments of sum to moments of product," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 542-554, March.
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