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.
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The authors are grateful to the anonymous referees for their valuable comments and careful reading of the manuscript.
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Śliwa, P., Schmid, W. Monitoring the cross-covariances of a multivariate time series. Metrika 61, 89–115 (2005). https://doi.org/10.1007/s001840400326
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DOI: https://doi.org/10.1007/s001840400326