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Monitoring the cross-covariances of a multivariate time series

Author

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  • Przemysław Śliwa
  • Wolfgang Schmid

Abstract

In this paper sequential procedures are proposed for jointly monitoring all elements of the covariance matrix at lag 0 of a multivariate time series. All control charts are based on exponential smoothing. As a measure of the distance between the target values and the actual values the Mahalanobis distance is used. It is distinguished between residual control schemes and modified control schemes. Several properties of these charts are proved assuming the target process to be a stationary Gaussian process. Within an extensive Monte Carlo study all procedures are compared with each other. As a measure of the performance of a control chart the average run length is used. An empirical example about Eastern European stock markets illustrates how the autocovariance and the cross-covariance structure of financial assets can be monitored by these methods. Copyright Springer-Verlag 2005

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:61:y:2005:i:1:p:89-115
    DOI: 10.1007/s001840400326
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    Citations

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    Cited by:

    1. Bock, David & Andersson, Eva & Frisén, Marianne, 2007. "Similarities and differences between statistical surveillance and certain decision rules in finance," Research Reports 2007:8, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    2. Jeffrey E. Jarrett & Xia Pan, 2007. "Monitoring Variability and Analyzing Multivariate Autocorrelated Processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(4), pages 459-469.
    3. 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.
    4. Jarrett, Jeffrey E. & Pan, Xia, 2007. "The quality control chart for monitoring multivariate autocorrelated processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3862-3870, May.

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