A1320
Title: Multiscale change detection for non-stationary time series
Authors: Fabian Mies - Delft University of Technology (Netherlands) [presenting]
Johann Koehne - University of Goettingen (Germany)
Abstract: To increase the power of a CUSUM-based test for structural breaks against short-lived changes, the tests may be localized for various bandwidths and aggregated into a so-called multiscale test statistic. This procedure has recently been shown to possess optimal detection properties against breaks of all sizes and durations. As an intricate multiple-testing procedure, the multiscale test requires control of the finite sample behavior of the process under investigation, which is usually ensured by imposing Gaussianity of the errors or by imposing sub-Gaussian tail bounds. However, the latter can lead to infeasible statistical methods as the sub-Gaussian norm can not be estimated reliably. The method of obtaining a feasible multiscale test is demonstrated via weak convergence arguments. To this end, suitable tightness results are derived for the functional central limit in Holder spaces. Probabilistically, a new kind of restricted weak convergence is discovered, which only holds in the tails of the distribution. The novel theory allows for the optimal detection properties of multiscale tests to be maintained and extended to non-stationary nonlinear time series via a suitable bootstrap scheme.
