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Factorisable sparse tail event curves

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  • Chao, Shih-Kang
  • Härdle, Wolfgang Karl
  • Yuan, Ming

Abstract

In this paper, we propose a multivariate quantile regression method which enables localized analysis on conditional quantiles and global comovement analysis on conditional ranges for high-dimensional data. The proposed method, hereafter referred to as FActorisable Sparse Tail Event Curves, or FASTEC for short, exploits the potential factor structure of multivariate conditional quantiles through nuclear norm regularization and is particularly suitable for dealing with extreme quantiles. We study both theoretical properties and computational aspects of the estimating procedure for FASTEC. In particular, we derive nonasymptotic oracle bounds for the estimation error, and develope an efficient proximal gradient algorithm for the non-smooth optimization problem incurred in our estimating procedure. Merits of the proposed methodology are further demonstrated through applications to Conditional Autoregressive Value-at-Risk (CAViaR) (Engle and Manganelli; 2004), and a Chinese temperature dataset.

Suggested Citation

  • Chao, Shih-Kang & Härdle, Wolfgang Karl & Yuan, Ming, 2015. "Factorisable sparse tail event curves," SFB 649 Discussion Papers 2015-034, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2015-034
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    References listed on IDEAS

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    1. Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
    2. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
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    5. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    6. A. Belloni & V. Chernozhukov & L. Wang, 2011. "Square-root lasso: pivotal recovery of sparse signals via conic programming," Biometrika, Biometrika Trust, vol. 98(4), pages 791-806.
    7. Ming Yuan & Ali Ekici & Zhaosong Lu & Renato Monteiro, 2007. "Dimension reduction and coefficient estimation in multivariate linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 329-346, June.
    8. Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June.
    9. Robert Serfling, 2002. "Quantile functions for multivariate analysis: approaches and applications," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(2), pages 214-232, May.
    10. White, Halbert & Kim, Tae-Hwan & Manganelli, Simone, 2015. "VAR for VaR: Measuring tail dependence using multivariate regression quantiles," Journal of Econometrics, Elsevier, vol. 187(1), pages 169-188.
    11. Manganelli, Simone & White, Halbert & Kim, Tae-Hwan, 2008. "Modeling autoregressive conditional skewness and kurtosis with multi-quantile CAViaR," Working Paper Series 957, European Central Bank.
    12. Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
    13. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    14. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Chao, Shih-Kang & Härdle, Wolfgang K. & Yuan, Ming, 2021. "Factorisable Multitask Quantile Regression," Econometric Theory, Cambridge University Press, vol. 37(4), pages 794-816, August.
    2. Hu, Junjie & López Cabrera, Brenda & Melzer, Awdesch, 2021. "Advanced statistical learning on short term load process forecasting," IRTG 1792 Discussion Papers 2021-020, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Härdle, Wolfgang Karl & Huang, Chen & Chao, Shih-Kang, 2016. "Factorisable sparse tail event curves with expectiles," SFB 649 Discussion Papers 2016-018, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. repec:hum:wpaper:sfb649dp2016-058 is not listed on IDEAS
    5. Wang, Weining & Yu, Lining & Wang, Bingling, 2020. "Tail Event Driven Factor Augmented Dynamic Model," IRTG 1792 Discussion Papers 2020-022, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    6. Chao, Shih-Kang & Härdle, Wolfgang Karl & Huang, Chen, 2016. "Multivariate factorisable sparse asymmetric least squares regression," SFB 649 Discussion Papers 2016-058, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. repec:hum:wpaper:sfb649dp2016-018 is not listed on IDEAS

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    More about this item

    Keywords

    high-dimensional data analysis; multivariate quantile regression; quantile regression; value-at-risk; nuclear norm; multi-task learning;
    All these keywords.

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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