Josua Gösmann

Sequential change point detection

We propose a new approach for sequential change point detection of a general class of parameters of a d-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. Our initial method is motivated by the likelihood-ratio test principle and applicable in closed-end scenarios. For the (mathematically more challenging) case of an open-end scenario we use a slightly modified version of the first statistic, which features an interesting and natural limit distribution under suitable regularity assumptions. We prove that for a large class of testing problems both detection schemes have asymptotic level alpha and are consistent. In the closed-end case, we also incorporate a self-normalization method such that estimation of the long-run variance is unnecessary. By means of a simulation study it is demonstrated that the new tests perform better than the currently available procedures. Finally our methodology is illustrated by small data examples dealing with stock prices during the dot-com bubble and the influence of the Brexit Referendum on exchange rates.