高维时间序列数据集在经济、金融、气象和神经科学等各个领域正变得越来越普遍。鉴于这种普遍存在的时间序列数据，令人惊讶的是，很少有关于变量筛选的作品讨论了时间序列设置，甚至更少的作品开发了利用时间序列数据的独特特征的方法。本文介绍了几种基于部分距离相关的无模型筛选方法，这些方法是专门为处理时间相关数据而发展起来的。方法开发的单变量模型，如非线性自回归模型与外源预测（NARX），和多变量模型，如线性或非线性VAR模型。我们的方法，这取决于时刻条件，以及在响应和协变量过程中的依赖强度，以及其他因素，证明了一定的筛选性能。依赖性通过函数依赖性测量来量化（Wu [Proc.Natl. Acad. Sci. USA 102（2005）14150-14154]）和$β$ -混合系数，并且结果依赖于对相依随机变量使用Nagaev和Rosenthal型不等式。通过广泛的模拟研究表明，我们的方法的有限样本性能，我们包括宏观经济预测的应用。
英文摘要：
High dimensional time series datasets are becoming increasingly common in various fields such as economics, finance, meteorology, and neuroscience. Given this ubiquity of time series data, it is surprising that very few works on variable screening discuss the time series setting, and even fewer works have developed methods which utilize the unique features of time series data. This paper introduces several model free screening methods based on the partial distance correlation and developed specifically to deal with time dependent data. Methods are developed both for univariate models, such as nonlinear autoregressive models with exogenous predictors (NARX), and multivariate models such as linear or nonlinear VAR models. Sure screening properties are proved for our methods, which depend on the moment conditions, and the strength of dependence in the response and covariate processes, amongst other factors. Dependence is quantified by functional dependence measures (Wu [Proc. Natl. Acad. Sci. USA 102 (2005) 14150-14154]) and $β$-mixing coefficients, and the results rely on the use of Nagaev and Rosenthal type inequalities for dependent random variables. Finite sample performance of our methods is shown through extensive simulation studies, and we include an application to macroeconomic forecasting.
Autoregressive with Slack Time Series Model for Forecasting a Partially-Observed Dynamical Time Series
The Institute of Statistical Mathematics（统计数理研究所）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Kyoto University（京都大学）；Hitotsubashi University（一桥大学）
