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Monitoring the mean and the variance of a stationary process

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  • S. Knoth
  • W. Schmid

Abstract

We deal with the problem of how deviations in the mean or the variance of a time series can be detected. Several simultaneous control charts are introduced which are based on EWMA (exponentially weighted moving average) statistics for the mean and the empirical variance. The combined X − S2 EWMA chart is extended to time series. Further simultaneous charts are considered. The comparision of these schemes shows that the residual attempt must be favored if a variance change is present.

Suggested Citation

  • S. Knoth & W. Schmid, 2002. "Monitoring the mean and the variance of a stationary process," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(1), pages 77-100, February.
    • Handle: RePEc:bla:stanee:v:56:y:2002:i:1:p:77-100
    DOI: 10.1111/1467-9574.03000
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    Cited by:

    1. Serel, Dogan A. & Moskowitz, Herbert, 2008. "Joint economic design of EWMA control charts for mean and variance," European Journal of Operational Research, Elsevier, vol. 184(1), pages 157-168, January.
    2. Frisén, Marianne & Andersson, Eva & Schiöler, Linus, 2009. "Sufficient reduction in multivariate surveillance," Research Reports 2009:2, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    3. Frisén, Marianne, 2011. "On multivariate control charts," Research Reports 2011:2, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    4. Marianne Frisen & Eva Andersson & Linus Schioler, 2010. "Evaluation of multivariate surveillance," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(12), pages 2089-2100.
    5. Frisén, Marianne, 2008. "Introduction to financial surveillance," Research Reports 2008:1, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    6. Frisén, Marianne, 2011. "Inference Principles For Multivariate Surveillance," Research Reports 2011:5, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    7. Sebastian Steinmetz, 2014. "EWMA charts: ARL considerations in case of changes in location and scale," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(4), pages 371-387, October.
    8. Frisén, Marianne, 2011. "Methods and evaluations for surveillance in industry, business, finance, and public health," Research Reports 2011:3, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    9. Christian Sonesson, 2003. "Evaluations of some Exponentially Weighted Moving Average methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(10), pages 1115-1133.

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