The effects of model parameter deviations on the variance of a linearly filtered time series |
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Authors: | Daniel W. Apley Hyun Cheol Lee |
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Affiliation: | 1. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208‐3119;2. Samsung Electronics, Semiconductor Business, Quality Assurance Department, Banwol‐Dong, Hwasung‐City, Gyeonggi‐Do, Korea 445‐701 |
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Abstract: | We consider a general linear filtering operation on an autoregressive moving average (ARMA) time series. The variance of the filter output, which is an important quantity in many applications, is not known with certainty because it depends on the true ARMA parameters. We derive an expression for the sensitivity (i.e., the partial derivative) of the output variance with respect to deviations in the model parameters. The results provide insight into the robustness of many common statistical methods that are based on linear filtering and also yield approximate confidence intervals for the output variance. We discuss applications to time series forecasting, statistical process control, and automatic feedback control of industrial processes. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010 |
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Keywords: | autoregressive moving average model time series forecasting, parameter uncertainty robustness control chart |
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