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CUSUM Control Schemes for Multivariate Time Series

In: Frontiers in Statistical Quality Control 8

Author

Listed:
  • Olha Bodnar

    (European University, Department of Statistics)

  • Wolfgang Schmid

    (European University, Department of Statistics)

Abstract

Summary Up to now only a few papers (e.g., Theodossiou (1993), Kramer and Schmid (1997)) dealt with the problem of detecting shifts in the mean vector of a multivariate time series. Here we generalize several well-known CUSUM charts for independent multivariate normal variables (Crosier (1988), Pignatiello and Runger (1990), Ngai and Zhang (2001)) to stationary Gaussian processes. We consider both modified control charts and residual charts. It is analyzed under which conditions the average run lengths of the charts do not depend on the covariance matrix of the white noise process. In an extensive Monte Carlo study these schemes are compared with the multivariate EWMA chart of Kramer and Schmid (1997). The underlying target process is a vector autoregressive moving average process of order (1,1). For measuring the performance of a control chart the average run length is used.

Suggested Citation

  • Olha Bodnar & Wolfgang Schmid, 2006. "CUSUM Control Schemes for Multivariate Time Series," Springer Books, in: Hans-Joachim Lenz & Peter-Theodor Wilrich (ed.), Frontiers in Statistical Quality Control 8, pages 55-73, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-1687-7_4
    DOI: 10.1007/3-7908-1687-6_4
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