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Monitoring Processes with Changing Variances

Author

Listed:
  • J. Keith Ord
  • Rob J. Hyndman
  • Anne B. Koehler
  • Ralph D. Snyder

Abstract

Statistical process control (SPC) has evolved beyond its classical applications in manufacturing to monitoring economic and social phenomena. This extension requires consideration of autocorrelated and possibly non-stationary time series. Less attention has been paid to the possibility that the variance of the process may also change over time. In this paper we use the innovations state space modeling framework to develop conditionally heteroscedastic models. We provide examples to show that the incorrect use of homoscedastic models may lead to erroneous decisions about the nature of the process. The framework is extended to include counts data, when we also introduce a new type of chart, the P-value chart, to accommodate the changes in distributional form from one period to the next.

Suggested Citation

  • J. Keith Ord & Rob J. Hyndman & Anne B. Koehler & Ralph D. Snyder, 2008. "Monitoring Processes with Changing Variances," Monash Econometrics and Business Statistics Working Papers 4/08, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2008-4
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2008/wp4-08.pdf
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    References listed on IDEAS

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    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 407-417, October.
    3. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 422-422, October.
    4. A B Koehler & N B Marks & R T O'connell, 2001. "EWMA control charts for autoregressive processes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(6), pages 699-707, June.
    5. Alwan, Layth C & Roberts, Harry V, 1988. "Time-Series Modeling for Statistical Process Control," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 87-95, January.
    6. Heinen, Andreas, 2003. "Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model," MPRA Paper 8113, University Library of Munich, Germany.
    7. Ord, J.K. & Koehler, A. & Snyder, R.D., 1995. "Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models," Monash Econometrics and Business Statistics Working Papers 4/95, Monash University, Department of Econometrics and Business Statistics.
    8. Jung, Robert C. & Kukuk, Martin & Liesenfeld, Roman, 2006. "Time series of count data: modeling, estimation and diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2350-2364, December.
    9. Cohen, Jacqueline & Garman, Samuel & Gorr, Wilpen, 2009. "Empirical calibration of time series monitoring methods using receiver operating characteristic curves," International Journal of Forecasting, Elsevier, vol. 25(3), pages 484-497, July.
    10. Xia Pan & Jeffrey Jarrett, 2004. "Applying State Space to SPC: Monitoring Multivariate Time Series," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(4), pages 397-418.
    11. Don G. Wardell & Herbert Moskowitz & Robert D. Plante, 1992. "Control Charts in the Presence of Data Correlation," Management Science, INFORMS, vol. 38(8), pages 1084-1105, August.
    12. Gary K. Grunwald & Kais Hamza & Rob J. Hyndman, 1997. "Some Properties and Generalizations of Non‐negative Bayesian Time Series Models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 615-626.
    13. Layth C. Alwan & Harry V. Roberts, 1995. "The Problem of Misplaced Control Limits," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(3), pages 269-278, September.
    14. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Chen, Yikai & Corr, David J. & Durango-Cohen, Pablo L., 2014. "Analysis of common-cause and special-cause variation in the deterioration of transportation infrastructure: A field application of statistical process control for structural health monitoring," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 96-116.

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    More about this item

    Keywords

    Control charts; count data; GARCH; heteroscedasticity; innovations; state space; statistical process control;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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