Detecting changes in a multiparameter exponential family by using adaptive CUSUM procedure

An adaptive cumulative sum (CUSUM) procedure is proposed to monitor parameter changes in a multiparameter exponential family where the change-point and postchange parameters are estimated adaptively. Approximations for average run lengths are derived. Monitoring changes in both mean and variance in the normal case is considered as an illustration. The conditional biases of the estimations for the change-point and postchange mean and variance is studied by simulation comparison with several other CUSUM procedures. An adaptive dam process by modifying the adaptive CUSUM process is used to detect and identify change points and change segments by using Citibank stock prices from 30 Dow Jones Industry Index.