Monitoring Processes with Changing Variances
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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| Length: | 26 pages |
| Date of creation: | Jul 2008 |
| Date of revision: | |
| Handle: | RePEc:gwc:wpaper:2008-004 |
| Contact details of provider: | Postal: Phone: (202) 994-6150 Fax: (202) 994-6147 Web page: http://www.gwu.edu/~forcpgmEmail: More information through EDIRC
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References listed on IDEAS
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- 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.
- 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.
- 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.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- 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.
- Heinen, Andreas, 2003.
"Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model,"
MPRA Paper
8113, University Library of Munich, Germany.
- HEINEN, Andréas, 2003. "Modelling time series count data: an autoregressive conditional Poisson model," CORE Discussion Papers 2003062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- 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 407-17, October.
- 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.
- 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.
- 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, October.
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