Abstract A vector-valued autoregressive time series model is considered. The autoregressive coefficients of the model are random with possible dependencies among them. Estimation of the large number of parameters in such models becomes costly with an increase in dimension. A sequential procedure is proposed that promises a significant gain in the sample size thus reduction in the cost of implementation. The procedure is also risk efficient in the sense that as the cost of sampling becomes negligible the asymptotic predictive risk of the proposed procedure reaches the oracle predictive risk corresponding to the best fixed sample size procedure that assumes the values of the nuisance parameters to be known. Extensive simulation results are presented to illustrate the properties of the proposed procedure in a finite sample.

中文翻译：

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多元随机系数自回归过程的风险有效序列估计

摘要 考虑向量值自回归时间序列模型。模型的自回归系数是随机的，它们之间可能存在依赖关系。随着维度的增加，对此类模型中大量参数的估计变得昂贵。提出了一种顺序程序，该程序有望显着增加样本量，从而降低实施成本。该过程也是风险有效的，因为随着采样成本变得可以忽略不计，所提议过程的渐近预测风险达到与最佳固定样本量过程相对应的预言机预测风险，该过程假设有害参数的值是已知的。提供了大量的模拟结果来说明所提出的程序在有限样本中的特性。