IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1808.02953.html
   My bibliography  Save this paper

Some Statistical Problems with High Dimensional Financial data

Author

Listed:
  • Arnab Chakrabarti
  • Rituparna Sen

Abstract

For high dimensional data, some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper, we explore these modifications. We start with the important problem of estimating high dimensional covariance matrix. Then we explore some of the important statistical techniques such as high dimensional regression, principal component analysis, multiple testing problems and classification. We describe some of the fast algorithms that can be readily applied in practice.

Suggested Citation

  • Arnab Chakrabarti & Rituparna Sen, 2018. "Some Statistical Problems with High Dimensional Financial data," Papers 1808.02953, arXiv.org.
    • Handle: RePEc:arx:papers:1808.02953
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1808.02953
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Peter Hall & J. S. Marron & Amnon Neeman, 2005. "Geometric representation of high dimension, low sample size data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 427-444, June.
    3. Adam J. Rothman, 2012. "Positive definite estimators of large covariance matrices," Biometrika, Biometrika Trust, vol. 99(3), pages 733-740.
    4. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    5. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    6. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
    7. Boginski, Vladimir & Butenko, Sergiy & Pardalos, Panos M., 2005. "Statistical analysis of financial networks," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 431-443, February.
    8. Theophilos Papadimitriou & Periklis Gogas & Georgios Antonios Sarantitis, 2014. "European Business Cycle Synchronization: A Complex Network Perspective," Springer Optimization and Its Applications, in: Valery A. Kalyagin & Panos M. Pardalos & Themistocles M. Rassias (ed.), Network Models in Economics and Finance, edition 127, pages 265-275, Springer.
    9. Fisher, Thomas J. & Sun, Xiaoqian, 2011. "Improved Stein-type shrinkage estimators for the high-dimensional multivariate normal covariance matrix," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1909-1918, May.
    10. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    11. N. Vandewalle & F. Brisbois & X. Tordoir, 2001. "Non-random topology of stock markets," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 372-374, March.
    12. Lingzhou Xue & Shiqian Ma & Hui Zou, 2012. "Positive-Definite ℓ 1 -Penalized Estimation of Large Covariance Matrices," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1480-1491, December.
    13. Brett Naul & Bala Rajaratnam & Dario Vincenzi, 2016. "The role of the isotonizing algorithm in Stein’s covariance matrix estimator," Computational Statistics, Springer, vol. 31(4), pages 1453-1476, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    2. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    3. Avagyan, Vahe & Nogales, Francisco J., 2015. "D-trace Precision Matrix Estimation Using Adaptive Lasso Penalties," DES - Working Papers. Statistics and Econometrics. WS 21775, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    5. Vahe Avagyan & Andrés M. Alonso & Francisco J. Nogales, 2018. "D-trace estimation of a precision matrix using adaptive Lasso penalties," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 425-447, June.
    6. Ding, Yi & Li, Yingying & Zheng, Xinghua, 2021. "High dimensional minimum variance portfolio estimation under statistical factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 502-515.
    7. Tae-Hwy Lee & Ekaterina Seregina, 2020. "Learning from Forecast Errors: A New Approach to Forecast Combination," Working Papers 202024, University of California at Riverside, Department of Economics.
    8. Yan Zhang & Jiyuan Tao & Zhixiang Yin & Guoqiang Wang, 2022. "Improved Large Covariance Matrix Estimation Based on Efficient Convex Combination and Its Application in Portfolio Optimization," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    9. Gautam Sabnis & Debdeep Pati & Anirban Bhattacharya, 2019. "Compressed Covariance Estimation with Automated Dimension Learning," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 466-481, December.
    10. Yuki Ikeda & Tatsuya Kubokawa, 2015. "Linear Shrinkage Estimation of Large Covariance Matrices with Use of Factor Models," CIRJE F-Series CIRJE-F-958, CIRJE, Faculty of Economics, University of Tokyo.
    11. Ikeda, Yuki & Kubokawa, Tatsuya & Srivastava, Muni S., 2016. "Comparison of linear shrinkage estimators of a large covariance matrix in normal and non-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 95-108.
    12. Ziqi Chen & Chenlei Leng, 2016. "Dynamic Covariance Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1196-1207, July.
    13. Shaoxin Wang & Hu Yang & Chaoli Yao, 2019. "On the penalized maximum likelihood estimation of high-dimensional approximate factor model," Computational Statistics, Springer, vol. 34(2), pages 819-846, June.
    14. Avagyan, Vahe & Nogales, Francisco J., 2014. "Improving the graphical lasso estimation for the precision matrix through roots ot the sample convariance matrix," DES - Working Papers. Statistics and Econometrics. WS ws141208, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Yu, Philip L.H. & Wang, Xiaohang & Zhu, Yuanyuan, 2017. "High dimensional covariance matrix estimation by penalizing the matrix-logarithm transformed likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 12-25.
    16. Choi, Young-Geun & Lim, Johan & Roy, Anindya & Park, Junyong, 2019. "Fixed support positive-definite modification of covariance matrix estimators via linear shrinkage," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 234-249.
    17. Jianqing Fan & Yuan Liao & Han Liu, 2016. "An overview of the estimation of large covariance and precision matrices," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.
    18. Ikeda, Yuki & Kubokawa, Tatsuya, 2016. "Linear shrinkage estimation of large covariance matrices using factor models," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 61-81.
    19. Li, Peili & Xiao, Yunhai, 2018. "An efficient algorithm for sparse inverse covariance matrix estimation based on dual formulation," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 292-307.
    20. Jianqing Fan & Xu Han, 2017. "Estimation of the false discovery proportion with unknown dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1143-1164, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1808.02953. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.