Order selection for same-realization predictions in autoregressive processes
自回归过程中同一实现预测的阶数选择AI 解读 ↓
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自回归过程中同一实现预测的阶数选择
- 研究问题
- 用已观测时间序列预测自身未来、而非预测独立复制序列时，AIC 及其变体是否仍具有渐近预测效率，存在哪些限制？
- 方法与思路
- 作者以无限阶自回归过程为基础，允许拟合阶数随样本增加，并引入技术条件处理选阶、参数估计与未来观测的依赖。
- 材料陈述的贡献
- 摘要称首次验证了 AIC 及其变体在所定义的同一实现预测中的渐近效率，并用模拟展示有限样本表现及该场景特有的限制。
- 阅读关注点
- 核对预测效率的正式定义、技术条件和允许的阶数增长范围，重点查明摘要提到的 AIC 限制及其与独立预测的差别。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；效率定义、技术条件和限制内容未展开，不能断言 AIC 对任意序列或预测目标最优。
原文摘要
Assume that observations are generated from an infinite-order autoregressive [AR(∞)] process. Shibata [Ann. Statist. 8 (1980) 147–164] considered the problem of choosing a finite-order AR model, allowing the order to become infinite as the number of observations does in order to obtain a better approximation. He showed that, for the purpose of predicting the future of an independent replicate, Akaike’s information criterion (AIC) and its variants are asymptotically efficient. Although Shibata’s concept of asymptotic efficiency has been widely accepted in the literature, it is not a natural property for time series analysis. This is because when new observations of a time series become available, they are not independent of the previous data. To overcome this difficulty, in this paper we focus on order selection for forecasting the future of an observed time series, referred to as same-realization prediction. We present the first theoretical verification that AIC and its variants are still asymptotically efficient (in the sense defined in Section 4) for same-realization predictions. To obtain this result, a technical condition, easily met in common practice, is introduced to simplify the complicated dependent structures among the selected orders, estimated parameters and future observations. In addition, a simulation study is conducted to illustrate the practical implications of AIC. This study shows that AIC also yields a satisfactory same-realization prediction in finite samples. On the other hand, a limitation of AIC in same-realization settings is pointed out. It is interesting to note that this limitation of AIC does not exist for corresponding independent cases.