通过稀疏PCA分析新冠疫情对股市的影响

doi:10.52396/JUST-2021-0102

中国科学技术大学学报 ›› 2021, Vol. 51 ›› Issue (5): 404-418.DOI: 10.52396/JUST-2021-0102

• 研究论文:管理科学与工程 • 上一篇下一篇

通过稀疏PCA分析新冠疫情对股市的影响

黎明, 温灿红^*

中国科学技术大学管理学院统计与金融系,安徽合肥 230026

收稿日期:2021-04-07 修回日期:2021-04-13 出版日期:2021-05-31 发布日期:2021-12-01
通讯作者: * E-mail:wench@ustc.edu.cn

Impact of COVID-19 pandemic on stock market via sparse principal component analysis

Li Ming, Wen Canhong^*

Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China

Received:2021-04-07 Revised:2021-04-13 Online:2021-05-31 Published:2021-12-01
Contact: * E-mail: wench@ustc.edu.cn

摘要/Abstract

摘要： 新冠疫情的爆发在全世界造成了严重的公共卫生和经济后果。评估新冠疫情对经济,尤其是股市的影响非常重要。为此,我们提出应用几种最先进的稀疏主成分分析(PCA)方法来分析2019年2月1日至2021年2月1日的沪深300指数股票数据,以揭示新冠疫情爆发的影响.将这段时间分为两个时期——2020年1月1日之前和之后,在此基础上,我们尝试提取主成分并构建投资组合.结果表明,在新冠疫情爆发之后,代表市场的主成分的比例有所下降.关于前两个主成分的构成,新冠疫情爆发后,起决定作用的股票集合有很大的不同.在新冠疫情之后,医疗保健行业的股票开始在沪深 300 指数的投资组合中发挥重要作用.与沪深 300 指数相比,稀疏 PCA 方法的前两个主成分可以在组成投资组合的股票集数量少得多的情况下获得更高的回报.综上所述,新冠疫情的爆发导致沪深 300 指数股票的主成分比例和构成发生了变化.

关键词: 新冠疫情, 稀疏主成分分析, 股票指数

Abstract: The COVID-19 pandemic has caused severe public health and economic consequences around the world. It is of great importance to evaluate the impact of the COVID-19 pandemic on the economy, especially the stock market. To this end, we proposed to use several state-of-art sparse principal component analysis (PCA) methods for the stock data of the CSI 300 index from February 1, 2019 to February 1, 2021. To show the influence of the outbreak of the COVID-19 pandemic, we divide this period into two periods, i.e., before and after January 1, 2020. Based on this division, we attempted to extract the principal components and construct portfolio accordingly. The results show that the proportion of principal components representing the market declined after the outbreak. For the constitution in the first two principal components, the important stock sets are substantially different after the outbreak. The stocks from the health care sector start to play an important role in the portfolio of the CSI 300 index after the outbreak. Compared with the CSI 300 index, the first two principal components from the sparse PCA methods can obtain higher returns with a much smaller set of stocks in the portfolio. In conclusion, the outbreak of the COVID-19 pandemic led to changes in both proportion and constitution of the principal component of the stocks in the CSI 300 index.

Key words: COVID-19 pandemic, sparse PCA, stock index

中图分类号:

F830.91

黎明, 温灿红. 通过稀疏PCA分析新冠疫情对股市的影响[J]. 中国科学技术大学学报, 2021, 51(5): 404-418.

LI Ming, WEN Canhong. Impact of COVID-19 pandemic on stock market via sparse principal component analysis[J]. Journal of University of Science and Technology of China, 2021, 51(5): 404-418.

参考文献

[1] Yang L. An application of principal component analysis to stock portfolio management. Christchurch, New Zealand: University of Canterbury, 2015.
[2] Cadima J, Jolliffe I T. Loading and correlations in the interpretation of principle components. Journal of Applied Statistics, 1995, 22(2): 203-214.
[3] Vines S. Simple principal components. Journal of the Royal Statistical Society: Series C (Applied Statistics), 2000, 49(4): 441-451.
[4] Ma Z. Sparse principal component analysis and iterative thresholding. Annals of Statistics, 2013, 41(2): 772-801.
[5] Jolliffe I T, Trendafilov N T, Uddin M. A modified principal component technique based on the LASSO. Journal of Computational and Graphical Statistics, 2003, 12(3): 531-547.
[6] d’Aspremont A, El Ghaoui L, Jordan M I, et al. A direct formulation for sparse PCA using semidefinite programming. SIAM Review, 2007, 49(3): 434-448.
[7] Journée M, Nesterov Y, Richtárik P, et al. Generalized power method for sparse principal component analysis. Journal of Machine Learning Research, 2010, 11(2): 517-553.
[8] Moghaddam B, Weiss Y, Avidan S. Spectral bounds for sparse PCA: Exact and greedy algorithms. In: Proceedings of the 18th International Conference on Neural Information Processing Systems. Cambridge, MA: MIT Press, 2005: 915-922.
[9] d’Aspremont A, Bach F, El Ghaoui L. Optimal solutions for sparse principal component analysis. Journal of Machine Learning Research, 2008, 9(7): 1269-1294.
[10] Croux C, Filzmoser P, Fritz H. Robust sparse principal component analysis. Technometrics, 2013, 55(2): 202-214.
[11] Shen H, Huang J Z. Sparse principal component analysis via regularized low rank matrix approximation. Journal of Multivariate Analysis, 2008, 99(6): 1015-1034.
[12] Zou H, Hastie T, Tibshirani R. Sparse principal component analysis. Journal of Computational and Graphical Statistics, 2006, 15(2): 265-286.
[13] Tipping M E, Bishop C M. Probabilistic principal component analysis. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 1999, 61(3): 611-622.
[14] Sigg C D, Buhmann J M. Expectation-maximization for sparse and non-negative PCA. In: Proceedings of the 25th International Conference on Machine Learning. New York: Association for Computing Machinery, 2008: 960-967.
[15] Witten D M, Tibshirani R, Hastie T. A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics, 2009, 10(3): 515-534.
[16] Friedman J, Hastie T, Tibshirani R, et al. The Elements of Statistical Learning. New York: Springer, 2001.
[17] Zou H, Hastie T. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2005, 67(2): 301-320.
[18] Avellaneda M. Hierarchical PCA and applications to portfolio management. https://ssrn.com/abstract=3467712.
[19] Hsu Y L, Huang P Y, Chen D T. Sparse principal component analysis in cancer research. Translational Cancer Research, 2014, 3(3): 182-190.
[20] Wen C, Zhang A, Quan S, et al. BeSS: An R package for best subset selection in linear, logistic and CoxPH models. Journal of Statistical Software, 2020, 94(1): 1-24.
[21] Bertsimas D, Cory-Wright R, Pauphilet J. Solving large-scale sparse PCA to certifiable (near) optimality. https://arxiv.org/abs/2005.05195.

通过稀疏PCA分析新冠疫情对股市的影响

Impact of COVID-19 pandemic on stock market via sparse principal component analysis

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