Sequential Control of Non-Stationary Processes by Nonparametric Kernel Control Charts

This paper studies nonparametric control charts to sequentially monitor dependent stochastic processes in continuous time with arbitrary but smooth drift functions m(t) to detect fast changes of m(t). Such methods are of particular interest when monitoring financial time series in order to detect rapid changes of the process mean. We provide a generalized framework for nonparametric process control where a process is regarded as out-of-control if the derivative of the process mean is to large. For a rich class of control charts based on linear smoothers it is shown how to design appropriate control charts guaranteeing an in-control average run length greather than or equal to a prescribed value. Further, a fundamental property of control charts concerning the average run length in the presence of positive autocorrelation, first estabilished for the EWMA chart applied to a Gaussian process, is extended to the case that it is applied to linear kernel smoothers. In addition, we study control charts based on local linear estimators. The performance of the proposed charts is compared by simulation studies