A0428
Title: Monitoring time series for relevant changes
Authors: Patrick Bastian - Ruhr-Universität Bochum (Germany) [presenting]
Abstract: The problem of sequentially testing is considered for changes in the mean parameter of a time series compared to a benchmark from an initial sample. This problem has been intensively studied in the literature, with most tests focusing on the null hypothesis of a constant mean versus the alternative hypothesis of a single change at an unknown time. However, in most applications, it seems unrealistic that either no change should occur at all or that, after a single change, the time series should remain stationary forever. A new setup is introduced, where the mean is modeled as a piecewise constant with arbitrarily many changes over time. Rather than testing for the presence of a change, the question is whether the evolving mean of the time series $\mu_n$ is within a narrow corridor around an initial value, i.e., $\mu_n \in [\mu_1-\Delta, \mu_1+\Delta]$ for all $n\ge 1$. The approach combines elements from multiple change-point detection with state-of-the-art monitoring procedures. A statistical challenge is the formulation of an adequate rejection rule because the risk of incurring a type-I error after a time point $n_0$ fundamentally depends on the unknown future of the time series for $n>n_0$.
