Simultaneous Estimation of Stable Parameters for Multiple Autoregressive Processes From Datasets of Nonuniform Sizes
提出一种有限样本理论，用于估计多个共享未知滞后阶数但样本量不同的稳定自回归过程的系数，并实现预测，通过类似分层重叠组套索的惩罚方法直接从数据中估计共同滞后阶数，证明估计过程具有稳定性，且估计和预测误差率优于已知结果。
ABSTRACT We develop a finite‐sample theory for estimating the coefficients and for the prediction of multiple stable autoregressive processes that (i) share an unknown lag order but (ii) can differ in their sample sizes. Our technique is based on penalisation similar to hierarchical, overlapping group‐Lasso but requires a new mathematical set‐up to accommodate (i) and (ii). The set‐up differs from existing work considerably, for example, in that we estimate the common lag order directly from the data rather than using extrinsic criteria. We prove that the estimated autoregressive processes enjoy stability, and we establish rates for both the estimation and prediction error that can outmatch the known rates in our setting. Our insights on lag selection and stability are also of interest in the case of individual autoregressive processes.