A comparative study on sequential detection of random mean change in multivariate normal data stream

• Published in: Sequential analysis Vol. 43; no. 4; pp. 477 - 496
• Main Authors: Wu, Yanhong, Wu, Wei Biao, Kim, Dong-Yun
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 01.10.2024; Taylor & Francis Ltd
• Subjects: Adaptive sampling; Comparative analysis; Comparative studies; CUSUM charts; Data transmission; Eigenvalues; Exponential weighted moving variance; False alarms; false detecting probability; generalized likelihood ratio; Likelihood ratio; Mean; moving largest eigenvalue; Multivariate analysis; power of detection; Sample variance; Variance
• ISSN: 0747-4946; 1532-4176
• DOI: 10.1080/07474946.2024.2418939

For the detection of random mean changes in a multivariate normal data stream, we explore and compare various direction-invariant monitoring charts. These include the (adaptive) largest eigenvalue charts employing exponential weighted moving variance (EWMV), the moving largest eigenvalue (MLE) based on moving sample variance, and both adaptive and windowed cumulative sum (CUSUM) charts with a reference value for the largest eigenvalue. The comparison involves assessing the power of detection (POD) given false detection probability (FDP) at a signal length and the average delay detection time (ADDT) given a false alarm rate (FAR) at a change time. Our primary contribution involves introducing the moving generalized likelihood ratio (MGLR) chart, which relies solely on the chi-square property of the adjusted generalized likelihood ratio. We provide simple approximations for FDP and FAR for design purposes. Our results indicate that the EWMV chart is recommended, and the MGLR chart performs effectively. Detection of volatility change in 30 Dow Jones Industrial stock prices is used for illustration.