This paper studies high-dimensional trend inference for piecewise smooth signals under nonstationary noise and asynchronous structural breaks by first detecting asynchronous changes without assuming stationarity and then further exploiting latent group structures to estimate trend functions. In the first step, we propose AJDN (Asynchronous Jump Detection under Nonstationary Noise), a multiscale framework for the identification and localization of jumps in high-dimensional time series. We show that AJDN consistently recovers the number of jumps with a prescribed asymptotic probability and achieves nearly optimal localization rates in the presence of asynchronicity and nonstationarity, both of which often violate the assumptions of existing high-dimensional change point methods and thereby deteriorate their performance.

翻译：暂无翻译