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Estimating the Variances of Autocorrelations Calculated from Financial Time Series

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  • Stephen J. Taylor

Abstract

Autocorrelation coefficients calculated from n observations are known to have variances approximately equal to 1/n, for a series of independent and identically distributed variables. The variances can be higher for a general uncorrelated process. Estimates of the variances are derived, assuming only that the process is uncorrelated with symmetric distributions. Results are presented for 17 financial time series. Most estimates exceed 2.5/n for daily returns from commodities, 1.6/n for currencies and 1.3/n for a share index. Standard tests for zero autocorrelation are therefore unreliable. Suitably rescaled data have autocorrelation variances close to 1/n.

Suggested Citation

  • Stephen J. Taylor, 1984. "Estimating the Variances of Autocorrelations Calculated from Financial Time Series," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(3), pages 300-308, November.
    • Handle: RePEc:bla:jorssc:v:33:y:1984:i:3:p:300-308
    DOI: 10.2307/2347707
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    Cited by:

    1. Luger, Richard, 2003. "Exact non-parametric tests for a random walk with unknown drift under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 115(2), pages 259-276, August.
    2. Dalla, Violetta & Giraitis, Liudas & Phillips, Peter C. B., 2022. "Robust Tests For White Noise And Cross-Correlation," Econometric Theory, Cambridge University Press, vol. 38(5), pages 913-941, October.
    3. Nankervis, John C. & Savin, N. E., 2010. "Testing for Serial Correlation: Generalized Andrews–Ploberger Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 246-255.
    4. Fiorentini, Gabriele & Sentana, Enrique, 2021. "New testing approaches for mean–variance predictability," Journal of Econometrics, Elsevier, vol. 222(1), pages 516-538.
    5. repec:adr:anecst:y:1991:i:24:p:01 is not listed on IDEAS
    6. Semenov, Andrei, 2008. "Testing the random walk hypothesis through robust estimation of correlation," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2504-2513, January.
    7. Xuexin Wang & Yixiao Sun, 2020. "An Asymptotic F Test for Uncorrelatedness in the Presence of Time Series Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 536-550, July.
    8. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    9. Stephen Taylor, 2000. "Stock index and price dynamics in the UK and the US: new evidence from a trading rule and statistical analysis," The European Journal of Finance, Taylor & Francis Journals, vol. 6(1), pages 39-69.
    10. Tim Bollerslev & Ray Y. Chou & Narayanan Jayaraman & Kenneth F. Kroner - L, 1991. "es modéles ARCH en finance : un point sur la théorie et les résultats empiriques," Annals of Economics and Statistics, GENES, issue 24, pages 1-59.

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