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雷达卡
摘要翻译：
我们提出了一个过程来确定公共因子空间的维数在一个大的，可能是非平稳的，数据集中。我们的程序旨在确定是否存在（以及有多少）公共因素(i)具有线性趋势，(ii)具有随机趋势，(iii)没有趋势，即平稳。我们的分析是基于这样一个事实，即当数据集的维数$N$发散时，适当缩放的数据协方差矩阵（对应于公共因子部分）的最大特征值发散，而其他特征值保持有界。因此，我们直接基于估计的特征值，提出了一种随机检验统计量，用于特征值发散的零值。这些测试只需要对数据进行最小的假设，而对相对偏离率$N$和$T$没有任何限制。蒙特卡罗证据表明，我们的方法具有非常好的有限样本性质，当没有公共因素时，明显地控制了竞争方法。我们通过对过去30年观察到的不同期限的美国债券收益率的应用来说明我们的方法。发现了一个共同的线性趋势和两个共同的随机趋势，并将其确定为经典的水平因子、斜率因子和曲率因子。
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英文标题：
《Determining the dimension of factor structures in non-stationary large
datasets》
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作者：
Matteo Barigozzi, Lorenzo Trapani
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最新提交年份：
2018
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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：
We propose a procedure to determine the dimension of the common factor space in a large, possibly non-stationary, dataset. Our procedure is designed to determine whether there are (and how many) common factors (i) with linear trends, (ii) with stochastic trends, (iii) with no trends, i.e. stationary. Our analysis is based on the fact that the largest eigenvalues of a suitably scaled covariance matrix of the data (corresponding to the common factor part) diverge, as the dimension $N$ of the dataset diverges, whilst the others stay bounded. Therefore, we propose a class of randomised test statistics for the null that the $p$-th eigenvalue diverges, based directly on the estimated eigenvalue. The tests only requires minimal assumptions on the data, and no restrictions on the relative rates of divergence of $N$ and $T$ are imposed. Monte Carlo evidence shows that our procedure has very good finite sample properties, clearly dominating competing approaches when no common factors are present. We illustrate our methodology through an application to US bond yields with different maturities observed over the last 30 years. A common linear trend and two common stochastic trends are found and identified as the classical level, slope and curvature factors.
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PDF链接：
https://arxiv.org/pdf/1806.03647
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