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Surveillance of the covariance matrix based on the properties of the singular Wishart distribution

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  • Bodnar, Olha
  • Bodnar, Taras
  • Okhrin, Yarema

Abstract

A methodology which allows applying the standard monitoring techniques for the mean behaviour of Gaussian processes in the detection of shifts in the covariance matrix is developed. Moreover, the proposed methodology allows the use of an estimator of the covariance matrix based on a single observation. An extensive simulation study reveals the advantages of the considered approach.

Suggested Citation

  • Bodnar, Olha & Bodnar, Taras & Okhrin, Yarema, 2009. "Surveillance of the covariance matrix based on the properties of the singular Wishart distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3372-3385, July.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:9:p:3372-3385
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    References listed on IDEAS

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    1. Przemysław Śliwa & Wolfgang Schmid, 2005. "Monitoring the cross-covariances of a multivariate time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(1), pages 89-115, February.
    2. Bodnar, Taras & Okhrin, Yarema, 2008. "Properties of the singular, inverse and generalized inverse partitioned Wishart distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2389-2405, November.
    3. Christian Sonesson & David Bock, 2003. "A review and discussion of prospective statistical surveillance in public health," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 166(1), pages 5-21, February.
    4. Eva Andersson & David Bock & Marianne Frisén, 2004. "Detection of Turning Points in Business Cycles," Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2004(1), pages 93-108.
    5. Messaoud, Amor & Weihs, Claus & Hering, Franz, 2008. "Detection of chatter vibration in a drilling process using multivariate control charts," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3208-3219, February.
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    Cited by:

    1. Taras Bodnar & Arjun Gupta, 2013. "An exact test for a column of the covariance matrix based on a single observation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 847-855, August.
    2. Golosnoy, Vasyl & Ragulin, Sergiy & Schmid, Wolfgang, 2011. "CUSUM control charts for monitoring optimal portfolio weights," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2991-3009, November.
    3. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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