Decoupling change-point detection based on characteristic functions: Methodology, asymptotics, subsampling and application

We study the problem of detecting changes in a location scale model. Our novel detector is based on sequential estimates of two indicators derived from the characteristic function (ch.f.), which allow to decouple the location from the scale problem. The asymptotic theory treats general weighted integrals of nonlinear functions of the real and imaginary parts of (sequential) estimates of the characteristic function and covers (functional) central limit theorems as well as the corresponding subsampling versions, where the latter allow for resampling-based estimation of control limits. In this way, we provide a unifying approach and provide a base for practical implementations of the procedures. Our results also reveal that the estimated indicators have different convergence rates. This explains the decoupling and clustering effects observed in practice and is also in contrast to the case of the sample mean and sample variance, which share the same convergence rate. Monte Carlo simulations show that the effect is also present in finite samples and that the proposed monitoring procedures are powerful, especially for small shifts. Our simulations also show that subsampling with calibration leads to accurate estimation of control limits even in small samples. Lastly, we illustrate our procedure by applying it to the monitoring of intraday climate data.