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The correlation structure of the sample autocovariance function for a particular class of time series with elliptically contoured distribution

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  • Genton, Marc G.

Abstract

In the context of time series, the classical estimator of the autocovariance function can be written as a quadratic form of the observations. If data have an elliptically contoured distribution with constant mean, then the correlation between the sample autocovariance function at two different lags is a function of the time design matrix and the covariance matrix of the process. When data have a regular support, an explicit formula for this correlation is available for a particular family of covariance matrices. Surprisingly, this correlation structure is exactly the same as the one for a Gaussian white noise.

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  • 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.
    • Handle: RePEc:eee:stapro:v:41:y:1999:i:2:p:131-137
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. De Gooijer, Jan G., 1980. "Exact moments of the sample autocorrelations from series generated by general arima processes of order (p, d, q), d=0 or 1," Journal of Econometrics, Elsevier, vol. 14(3), pages 365-379, December.
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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. Genton, Marc G. & Gorsich, David J., 2002. "Nonparametric variogram and covariogram estimation with Fourier-Bessel matrices," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 47-57, November.
    3. Genton, Mark G. & Ruiz-Gazen, Anne, 2009. "Visualizing Influential Observations in Dependent Data," TSE Working Papers 09-051, Toulouse School of Economics (TSE).
    4. Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.

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