The multiple filter test for change point detection in time series

Abstract

A framework for the detection of change points in the expectation in sequences of random variables is presented. Specifically, we investigate time series with general distributional assumptions that may show an unknown number of change points in the expectation occurring on multiple time scales and that may also contain change points in other parameters. To that end we propose a multiple filter test (MFT) that tests the null hypothesis of constant expectation and, in case of rejection of the null hypothesis, an algorithm that estimates the change points. The MFT has three important benefits. First, it allows for general distributional assumptions in the underlying model, assuming piecewise sequences of i.i.d. random variables, where also relaxations with regard to identical distribution or independence are possible. Second, it uses a MOSUM type statistic and an asymptotic setting in which the MOSUM process converges weakly to a functional of a Brownian motion which is then used to simulate the rejection threshold of the statistical test. This approach enables a simultaneous application of multiple MOSUM processes which improves the detection of change points that occur on different time scales. Third, we also show that the method is practically robust against changes in other distributional parameters such as the variance or higher order moments which might occur with or even without a change in expectation. A function implementing the described test and change point estimation is available in the R package MFT.