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Exact General‐Lag Serial Correlation Moments And Approximate Low‐Lag Partial Correlation Moments For Gaussian White Noise

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  • Oliver D. Anderson

Abstract

. Given series realizations of length n generated by a Gaussian white noise process, we use formulae for the moments about zero of the serial covariances to obtain all the non‐centred and central moments up to order 4 for, first, the serial correlations exactly (all lags) and, then, the low‐lag partial correlations approximately (mainly to O(n‐3)). The results agree with empirical values obtained by simulation for n= 100.

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  • 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.
    • Handle: RePEc:bla:jtsera:v:14:y:1993:i:6:p:551-574
    DOI: 10.1111/j.1467-9892.1993.tb00166.x
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    Cited by:

    1. Kim, Hyoung-Moon, 2008. "A note on scale mixtures of skew normal distribution," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1694-1701, September.
    2. Paolella, Marc S., 2003. "Computing moments of ratios of quadratic forms in normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 313-331, March.
    3. Joanna Olbryś & Elżbieta Majewska, 2014. "Implications of market frictions: serial correlations in indexes on the emerging stock markets in Central and Eastern Europe," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(1), pages 51-70.
    4. Genton, Marc G., 1999. "The correlation structure of the sample autocovariance function for a particular class of time series with elliptically contoured distribution," Statistics & Probability Letters, Elsevier, vol. 41(2), pages 131-137, January.
    5. Kan, Raymond & Wang, Xiaolu, 2010. "On the distribution of the sample autocorrelation coefficients," Journal of Econometrics, Elsevier, vol. 154(2), pages 101-121, February.
    6. A. C. C. Kwan, 2003. "Sample partial autocorrelations and portmanteau tests for randomness," Applied Economics Letters, Taylor & Francis Journals, vol. 10(10), pages 605-609.

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