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:在各种应用的推动下,高维时间序列已成为一个积极的研究课题,特别是最近出现了几种方法和有限抽样理论,用于已知滞后的单个稳定的自动递减进程。相反,我们考虑的是多重稳定的自动递减进程,这些进程具有未知的滞后期。我们利用不同进程的信息同时选择滞后期和估计参数。我们证明,估计过程是稳定的,我们为预测错误确定了率,这可以超过我们设定的已知速率。我们对滞后期选择和稳定性的洞察力对于个体自动递减进程来说也是有意义的。</s>