The optimized CUSUM and EWMA multi-charts for jointly detecting a range of mean and variance change

ABSTRACT

This article considers the problem of jointly monitoring the mean and variance of a process by multi-chart schemes. Multi-chart is a combination of several single charts which detects changes in a process quickly. Asymptotic analyses and simulation studies show that the optimized CUSUM multi-chart has optimal performance than optimized EWMA multi-chart in jointly detecting mean and variance shifts in an $i.i.d.$ normal observation. A real example that monitors the changes in IBM's stock returns (mean) and risks (variance) is used to demonstrate the performance of the above two multi-charts. The proposed method has been compared to a benchmark and it performed better.

Keywords:

• Mean–variance monitoring
• optimized CUSUM & EWMA multi-charts
• IBM

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by National Basic Research Program of China (973 Program, 2015CB856004) and the National Natural Science Foundation of China (11531001).