J. Keith Ord, Anne B. Koehler, Ralph D. Snyder and Rob J. Hyndman,
International Journal of Forecasting (2009), 25(3), 518-525.
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.
Keywords: control charts, count data, GARCH, heteroscedasticity, innovations, state space, statistical process control