英文标题：
《Random matrix approach to estimation of high-dimensional factor models》
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作者：
Joongyeub Yeo, George Papanicolaou
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最新提交年份：
2017
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英文摘要：
In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to estimate high-dimensional factor models, using the empirical spectral density of residuals. The spectrum of covariance matrices from financial data typically exhibits two characteristic aspects: a few spikes and bulk. The former represent factors that mainly drive the features and the latter arises from idiosyncratic noise. Motivated by these two aspects, we consider a minimum distance between two spectrums; one from a covariance structure model and the other from real residuals of financial data that are obtained by subtracting principal components. Our method simultaneously provides estimators of the number of factors and information about correlation structures in residuals. Using free random variable techniques, the proposed algorithm can be implemented and controlled effectively. Monte Carlo simulations confirm that our method is robust to noise or the presence of weak factors. Furthermore, the application to financial time-series shows that our estimators capture essential aspects of market dynamics.
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中文摘要：
在处理高维数据集时，因子模型通常有助于降维。因子模型的估计在各个领域都得到了积极的研究。在本文的第一部分中，我们提出了一种利用残差的经验谱密度估计高维因子模型的新方法。金融数据协方差矩阵的频谱通常表现出两个特征方面：少量峰值和大量。前者代表主要驱动特征的因素，后者则来自于特殊噪声。出于这两个方面的考虑，我们考虑了两个光谱之间的最小距离；一个来自协方差结构模型，另一个来自通过减去主成分获得的金融数据的实际残差。我们的方法同时提供了因子数量的估计量和残差中相关结构的信息。利用自由随机变量技术，该算法可以有效地实现和控制。蒙特卡罗模拟证实，我们的方法对噪声或弱因素的存在具有鲁棒性。此外，对金融时间序列的应用表明，我们的估计量捕捉到了市场动态的基本方面。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Physics 物理学
二级分类：Data Analysis, Statistics and Probability 数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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