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：本文研究在非平稳噪声和非同步结构突变下，分段平滑信号的高维趋势推断问题。该方法首先在不假设平稳性的情况下检测非同步变化，然后进一步利用潜在分组结构来估计趋势函数。在第一步中，我们提出AJDN（非平稳噪声下的非同步跳跃检测），这是一个用于高维时间序列中跳跃识别与定位的多尺度框架。我们证明，AJDN能以预设的渐近概率一致地恢复跳跃数量，并在存在非同步性和非平稳性的情况下达到近乎最优的定位速率——这两种特性通常违反现有高维变点方法的假设，从而降低其性能。