Abstract
We consider the problem of detecting jumps 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 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. For a wide class of non-stationary time series models and trend functions, the proposed method is shown to be able to detect all jump points within a nearly optimal range with a prescribed probability asymptotically under mild conditions. For a time series of length n, the computational complexity of the proposed method is for each scale and overall, where ϵ is an arbitrarily small positive constant. Numerical studies show that the proposed jump testing and estimation method performs robustly and accurately under complex temporal dynamics.
Acknowledgments
The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper. Weichi Wu was supported by BJNSFZ190001, NSFC 12271287 and 11901337. Zhou’s research was supported by NSERC of Canada.
Citation
Weichi Wu. Zhou Zhou. "Multiscale jump testing and estimation under complex temporal dynamics." Bernoulli 30 (3) 2372 - 2398, August 2024. https://doi.org/10.3150/23-BEJ1677
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