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Monitoring Processes with Changing Variances

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  • J. Keith Ord

    ()
    (McDonough School of Business, Georgetown University,)

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.

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File URL: http://www.gwu.edu/~forcpgm/2008-004.pdf
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Bibliographic Info

Paper provided by The George Washington University, Department of Economics, Research Program on Forecasting in its series Working Papers with number 2008-004.

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Length: 26 pages
Date of creation: Jul 2008
Date of revision:
Handle: RePEc:gwc:wpaper:2008-004

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Keywords: control charts; count data; GARCH; heteroscedasticity; innovations; state space; statistical process control;

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  1. Cohen, Jacqueline & Garman, Samuel & Gorr, Wilpen, 2009. "Empirical calibration of time series monitoring methods using receiver operating characteristic curves," International Journal of Forecasting, Elsevier, Elsevier, vol. 25(3), pages 484-497, July.
  2. Don G. Wardell & Herbert Moskowitz & Robert D. Plante, 1992. "Control Charts in the Presence of Data Correlation," Management Science, INFORMS, INFORMS, vol. 38(8), pages 1084-1105, August.
  3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
  4. Xia Pan & Jeffrey Jarrett, 2004. "Applying State Space to SPC: Monitoring Multivariate Time Series," Journal of Applied Statistics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 31(4), pages 397-418.
  5. 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, Monash University, Department of Econometrics and Business Statistics 4/95, Monash University, Department of Econometrics and Business Statistics.
  6. Alwan, Layth C & Roberts, Harry V, 1988. "Time-Series Modeling for Statistical Process Control," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 6(1), pages 87-95, January.
  7. HEINEN, Andréas, 2003. "Modelling time series count data: an autoregressive conditional Poisson model," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2003062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 7(4), pages 407-17, October.
  9. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations: Reply," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 7(4), pages 422, October.
  10. Jung, Robert C. & Kukuk, Martin & Liesenfeld, Roman, 2006. "Time series of count data: modeling, estimation and diagnostics," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 51(4), pages 2350-2364, December.
  11. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, 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, Elsevier, vol. 59(C), pages 96-116.

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