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Surveillance of the mean behavior of multivariate time series

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  • Olha Bodnar
  • Wolfgang Schmid

Abstract

In this paper several cumulative sum (CUSUM) charts for the mean of a multivariate time series are introduced. We extend the control schemes for independent multivariate observations of crosier [Technometrics (1988) Vol. 30, pp. 187–194], pignatiello and runger [Journal of Quality Technology (1990) Vol. 22, pp. 173–186], and ngai and zhang [Statistica Sinica (2001) Vol. 11, pp. 747–766] to multivariate time series by taking into account the probability structure of the underlying stochastic process. We consider modified charts and residual schemes as well. It is analyzed under which conditions these charts are directionally invariant. In an extensive Monte Carlo study these charts are compared with the CUSUM scheme of theodossiu [Journal of the American Statistical Association (1993) Vol. 88, pp. 441–448], the multivariate exponentially weighted moving‐average (EWMA) chart of kramer and schmid [Sequential Analysis (1997) Vol. 16, pp. 131–154], and the control procedures of bodnar and schmid [Frontiers of Statistical Process Control (2006) Physica, Heidelberg]. As a measure of the performance, the maximum expected delay is used.

Suggested Citation

  • Olha Bodnar & Wolfgang Schmid, 2007. "Surveillance of the mean behavior of multivariate time series," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 383-406, November.
    • Handle: RePEc:bla:stanee:v:61:y:2007:i:4:p:383-406
    DOI: 10.1111/j.1467-9574.2007.00365.x
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    Cited by:

    1. Taras Lazariv & Wolfgang Schmid, 2019. "Surveillance of non-stationary processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 305-331, September.
    2. Robert Garthoff & Philipp Otto, 2018. "Verfahren zur Überwachung räumlicher autoregressiver Prozesse mit externen Regressoren [Statistical surveillance of spatial autoregressive processes with exogenous regressors]," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 12(2), pages 107-133, September.
    3. Robert Garthoff, 2014. "Sequentielle Überwachung von Finanzzeitreihen anhand von Residuenkarten," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 8(3), pages 91-113, September.
    4. Robert Garthoff & Iryna Okhrin & Wolfgang Schmid, 2014. "Statistical surveillance of the mean vector and the covariance matrix of nonlinear time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 225-255, July.
    5. 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.

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