Challenges in Monitoring Non-stationary Time Series

Abstract

Different approaches for monitoring non-stationary processes are discussed. Besides the transformation method, a more general procedure is described which makes use of the probability structure of the underlying in-control process. Here, the in-control process is assumed to be a multivariate state-space process. The out-of-control state is described by a general change point model which covers shifts and drifts in the components. Control charts with a reference vector are derived using the likelihood ratio, the sequential probability ratio, and the Shiryaev–Roberts approach. Moreover, the generalized likelihood ratio, the generalized sequential probability ratio, and the generalized modified Shiryaev–Roberts approach are used to obtain charts without reference parameters. All the introduced schemes are compared with each other assuming that a univariate unit root process with drift is present. We make use of several measures of the performance of control charts, such as the average run length, the worst average delay, and the limit average delay. This chapter also analyses how the charts with a reference parameter depend on the choice of this quantity.