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Higher Order Moments Of Sample Autocovariances And Sample Autocorrelations From An Independent Time Series

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  • Oliver D. Anderson
  • Zhao‐Guo Chen

Abstract

. Given length‐n sampled time series, generated by an independent distributed process, in this paper we treat the problem of determining the greatest order, in n, that moments of the sample autocovariances and sample autocorrelations can attain. For the sample autocovariance moments, we achieve quite general results; but, for the autocorrelation moments, we restrict study to Gaussian white noise (normal, independent and identically distributed). Our main theorem relates to the cross‐moments of the non‐centred sample autocovariances, but we also establish a relation between these and the corresponding moments for the centred sample autocovariances.

Suggested Citation

  • Oliver D. Anderson & Zhao‐Guo Chen, 1996. "Higher Order Moments Of Sample Autocovariances And Sample Autocorrelations From An Independent Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(4), pages 323-331, July.
    • Handle: RePEc:bla:jtsera:v:17:y:1996:i:4:p:323-331
    DOI: 10.1111/j.1467-9892.1996.tb00280.x
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    Cited by:

    1. 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.
    2. Kim, Hyoung-Moon, 2008. "A note on scale mixtures of skew normal distribution," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1694-1701, September.

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