摘要翻译：
在无限阶自回归(AR($infty$))模型中，研究了Rissanen累积预测误差(APE)准则的一种改进APE$_{\\delta_n}$的预测能力。APE$_{\\delta_n}$不是从一开始就累加顺序预测误差的平方，而是通过对阶段$n\delta_n$中的这些平方误差求和来获得，其中$n$是样本量，$1/n\leq\delta_n\leq1-(1/n)$可能取决于$n$。在一定的正则性条件下，给出了阶数为APE$_{\\delta_n}$的AR预测器的均方预测误差(MSPE)的渐近表达式。该表达式表明，APE$_{\delta_n}$的预测性能可能会因$\delta_n$的选择而发生显著变化。另一个有趣的发现是，当$\delta_n$以一定的速率接近1时，ape$_{\delta_n}$在大多数实际情况下都能达到渐近效率。从MSPE的观点出发，建立了APE$_{\\delta_n}$与一个带有适当惩罚项的信息准则的渐近等价性。这为理解基于信息和预测的模型选择标准提供了新的视角。最后，对于允许AR($\infty$)模型退化为有限自回归的情形，我们给出了第一个渐近效率的结果。
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英文标题：
《Accumulated prediction errors, information criteria and optimal
  forecasting for autoregressive time series》
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作者：
Ching-Kang Ing
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  The predictive capability of a modification of Rissanen's accumulated prediction error (APE) criterion, APE$_{\delta_n}$, is investigated in infinite-order autoregressive (AR($\infty$)) models. Instead of accumulating squares of sequential prediction errors from the beginning, APE$_{\delta_n}$ is obtained by summing these squared errors from stage $n\delta_n$, where $n$ is the sample size and $1/n\leq \delta_n\leq 1-(1/n)$ may depend on $n$. Under certain regularity conditions, an asymptotic expression is derived for the mean-squared prediction error (MSPE) of an AR predictor with order determined by APE$_{\delta_n}$. This expression shows that the prediction performance of APE$_{\delta_n}$ can vary dramatically depending on the choice of $\delta_n$. Another interesting finding is that when $\delta_n$ approaches 1 at a certain rate, APE$_{\delta_n}$ can achieve asymptotic efficiency in most practical situations. An asymptotic equivalence between APE$_{\delta_n}$ and an information criterion with a suitable penalty term is also established from the MSPE point of view. This offers new perspectives for understanding the information and prediction-based model selection criteria. Finally, we provide the first asymptotic efficiency result for the case when the underlying AR($\infty$) model is allowed to degenerate to a finite autoregression.
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PDF链接：
https://arxiv.org/pdf/708.2373