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摘要翻译：
本文提出了一种建立高维单位根时间序列因子模型的新方法，它假定一个$P$维单位根过程是一组单位根过程、一组动态相关的平稳公因子和一些特殊的白噪声分量的非奇异线性变换。对于平稳分量，我们假设因子过程捕捉时间相关性，而特殊白噪声序列与因子共同解释截面相关性。非奇异线性加载空间的估计分两步进行。首先，我们利用非负定矩阵的特征分析来区分单位根过程和平稳过程，并用一种修正的方法来确定单位根的个数。然后，我们使用另一个特征分析和投影主成分分析来识别平稳公因子和白噪声序列。我们提出了一种新的方法来确定白噪声序列的个数，从而确定平稳公因子的个数，并建立了该方法在固定和发散两种情况下随样本量N$增加的渐近性质，并用仿真和实例证明了该方法在有限样本中的性能。本文还将所提因子的预测能力与文献中常用因子的预测能力进行了比较，发现该方法对台湾508维PM$_{2.5}$序列的样本外预测有较好的效果。
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英文标题：
《Modeling High-Dimensional Unit-Root Time Series》
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作者：
Zhaoxing Gao, Ruey S. Tsay
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最新提交年份：
2020
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
This paper proposes a new procedure to build factor models for high-dimensional unit-root time series by postulating that a $p$-dimensional unit-root process is a nonsingular linear transformation of a set of unit-root processes, a set of stationary common factors, which are dynamically dependent, and some idiosyncratic white noise components. For the stationary components, we assume that the factor process captures the temporal-dependence and the idiosyncratic white noise series explains, jointly with the factors, the cross-sectional dependence. The estimation of nonsingular linear loading spaces is carried out in two steps. First, we use an eigenanalysis of a nonnegative definite matrix of the data to separate the unit-root processes from the stationary ones and a modified method to specify the number of unit roots. We then employ another eigenanalysis and a projected principal component analysis to identify the stationary common factors and the white noise series. We propose a new procedure to specify the number of white noise series and, hence, the number of stationary common factors, establish asymptotic properties of the proposed method for both fixed and diverging $p$ as the sample size $n$ increases, and use simulation and a real example to demonstrate the performance of the proposed method in finite samples. We also compare our method with some commonly used ones in the literature regarding the forecast ability of the extracted factors and find that the proposed method performs well in out-of-sample forecasting of a 508-dimensional PM$_{2.5}$ series in Taiwan.
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PDF链接：
https://arxiv.org/pdf/2005.03496
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