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. In the second step, we augment AJDN with a homogeneity pursuit step and obtain AJDN-H, which identifies latent groups of dimensions that share common jump structures and trend parameters given the detected jumps. This allows for efficient information pooling and improves the accuracy of trend estimation under both asynchronicity and nonstationarity. The robustness and finite-sample performance of the proposed methodology are examined by extensive simulation studies. An application to financial data demonstrates the practical utility of the AJDN-H framework in complex, high-dimensional settings.

翻译：本文研究在非平稳噪声与异步结构突变条件下，对分段平滑信号进行高维趋势推断，通过在不假定平稳性的前提下率先检测异步突变，并进一步利用潜在群组结构估计趋势函数。第一步，我们提出AJDN（非平稳噪声下的异步跳跃检测）——一种用于高维时间序列突变识别与定位的多尺度框架。研究表明，AJDN能以预设渐近概率一致恢复突变数量，并在异步性与非平稳性同时存在时实现近乎最优的定位速率；而现有高维变点方法常因违反上述假设导致性能下降。第二步，我们在AJDN中引入同质性追踪步骤获得AJDN-H，该方法能在检测到突变后识别共享共同突变结构与趋势参数的潜在维度群组。这实现了高效信息汇集，并提升异步与非平稳条件下趋势估计的精度。通过大量仿真研究检验所提方法的稳健性与有限样本性能。金融数据应用验证了AJDN-H框架在复杂高维场景中的实用价值。