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Monitoring change point for diffusion parameter based on discretely observed sample from stochastic differential equation models
Author(s) -
Lee Sangyeol,
Guo Meihui
Publication year - 2014
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2064
Subject(s) - stochastic differential equation , control chart , statistic , computer science , percentile , variance (accounting) , ewma chart , control limits , mathematics , sample size determination , chart , limit (mathematics) , mathematical optimization , statistics , process (computing) , mathematical analysis , accounting , business , operating system
Stochastic differential equation (SDE) models are useful in describing complex dynamical systems in science and engineering. In this study, we consider a monitoring procedure for an early detection of dispersion parameter change in SDE models. The proposed scheme provides a useful diagnostic analysis for phase I retrospective study and develops a flexible and effective control chart for phase II prospective monitoring. A standardized control chart is constructed, and a bootstrap method is used to estimate the mean and variance of the monitoring statistic. The control limit is obtained as an upper percentile of the maximum value of a standard Wiener process. The proposed procedure appears to have a manageable computational complexity for online implementation and also to be effective in detecting changes. We also investigate the performance of the exponentially weighted mean squared control charts for the continuous SDE processes. A simulation method is used to study the empirical sizes and the average run length characteristics of the proposed scheme, which also demonstrates the effectiveness of our method. Finally, we provide an empirical example for illustration. Copyright © 2014 John Wiley & Sons, Ltd.