Motivated by a variety of applications, high-dimensional time series have become an active topic of research. In particular, several methods and finite-sample theories for individual stable autoregressive processes with known lag have become available very recently. We, instead, consider multiple stable autoregressive processes that share an unknown lag. We use information across the different processes to simultaneously select the lag and estimate the parameters. We prove that the estimated process is stable, and we establish rates for the forecasting error that can outmatch the known rate in our setting. Our insights on the lag selection and the stability are also of interest for the case of individual autoregressive processes.

翻译：受多种应用驱动，高维时间序列已成为研究热点。特别地，针对已知滞后的单变量稳定自回归过程，近期已涌现出多种方法及有限样本理论。然而，我们考虑的是共享未知滞后参数的多变量稳定自回归过程。通过利用不同过程间的信息，我们同步实现滞后选择与参数估计。我们证明了所估计过程的稳定性，并建立了预报误差的收敛速率，该速率在特定场景下可超越已知的最优结果。此外，关于滞后选择与稳定性的研究见解对单变量自回归过程同样具有参考价值。