MACE: Multiscale Abrupt Change Estimation Under Complex Temporal Dynamics
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We consider the problem of detecting abrupt changes in an otherwise smoothly evolving trend whilst the covariance and higher-order structures of the system can experience both smooth and abrupt changes over time. The number of abrupt change 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 abrupt change 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(nlog^1+ϵ n) overall, where ϵ 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 multiscale change point detection methods.
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