Monitoring Change Point for Diffusion Parameter Based on Discretely Observed Sample from SDE Models

• Activity Number: 426
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Meihui Guo*+ and Sangyeol Lee
• Companies: National Sun Yat-Sen University and Seoul National University
• Keywords: Discretely observed sample ; EWMS control chart ; Hypothesis testing ; Model validation ; Standardized control chart

Abstract

In this paper, we consider a monitoring procedure for an early detection of the dispersion parameter changes 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 or a regression 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 on-line implementation and also to be effective in detecting changes. We also investigate the performance of the EWMS (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 present an empirical example for illustration.