B1335
Title: MACE: Multiscale abrupt change estimation under complex temporal dynamics
Authors: Weichi Wu - Tsinghua University (China) [presenting]
Zhou Zhou - University of Toronto (Canada)
Abstract: The focus is on the problem of detecting abrupt changes in trend whilst the covariance and higher-order structures of the system can experience both smooth and abrupt changes over time. The number of jump points is allowed to diverge to infinity with the jump sizes possibly shrinking to zero. The method is based on a multiscale application of an optimal jump-pass filter to the time series, where the scales are dense between admissible lower and upper bounds. The MACE method is shown to be able to detect all jump points within a nearly optimal range with a prescribed probability asymptotically. For a time series of length $n$, the computational complexity of MACE is $O(n)$ for each scale and $O(n\log^{1+\epsilon} n)$ overall, where $\epsilon$ is an arbitrarily small positive constant. Simulations and data analysis show that, under complex temporal dynamics, MACE performs favourably compared with some of the state-of-the-art change point detection methods.
