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Matching a distribution by matching quantiles estimation

Author

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  • Sgouropoulos, Nikolaos
  • Yao, Qiwei
  • Yastremiz, Claudia

Abstract

Motivated by the problem of selecting representative portfolios for backtesting counterparty credit risks, we propose a matching quantiles estimation (MQE) method for matching a target distribution by that of a linear combination of a set of random variables. An iterative procedure based on the ordinary least squares estimation (OLS) is proposed to compute MQE. MQE can be easily modified by adding a LASSO penalty term if a sparse representation is desired, or by restricting the matching within certain range of quantiles to match a part of the target distribution. The convergence of the algorithm and the asymptotic properties of the estimation, both with or without LASSO, are established. A measure and an associated statistical test are proposed to assess the goodness-of-match. The finite sample properties are illustrated by simulation. An application in selecting a counterparty representative portfolio with a real data set is reported. The proposed MQE also finds applications in portfolio tracking, which demonstrates the usefulness of combining MQE with LASSO.

Suggested Citation

  • Sgouropoulos, Nikolaos & Yao, Qiwei & Yastremiz, Claudia, 2015. "Matching a distribution by matching quantiles estimation," LSE Research Online Documents on Economics 57221, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:57221
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    File URL: http://eprints.lse.ac.uk/57221/
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    References listed on IDEAS

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    1. Lamont, Owen A., 2001. "Economic tracking portfolios," Journal of Econometrics, Elsevier, vol. 105(1), pages 161-184, November.
    2. Gneiting, Tilmann, 2011. "Quantiles as optimal point forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 197-207, April.
    3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    4. Gneiting, Tilmann, 2011. "Quantiles as optimal point forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 197-207.
    5. Sergio Firpo & Nicole M. Fortin & Thomas Lemieux, 2009. "Unconditional Quantile Regressions," Econometrica, Econometric Society, vol. 77(3), pages 953-973, May.
    6. Jianqing Fan & Jingjin Zhang & Ke Yu, 2012. "Vast Portfolio Selection With Gross-Exposure Constraints," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 592-606, June.
    7. Dose, Christian & Cincotti, Silvano, 2005. "Clustering of financial time series with application to index and enhanced index tracking portfolio," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 145-151.
    8. repec:ulb:ulbeco:2013/136280 is not listed on IDEAS
    9. Dominicy, Yves & Veredas, David, 2013. "The method of simulated quantiles," Journal of Econometrics, Elsevier, vol. 172(2), pages 235-247.
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    Cited by:

    1. Jacobi, Arie & Tzur, Joseph, 2021. "Wealth Distribution across Countries: Quality of Weibull, Dagum and Burr XII in Estimating Wealth over Time," Finance Research Letters, Elsevier, vol. 43(C).
    2. Qin, Shanshan & Wu, Yuehua, 2020. "General matching quantiles M-estimation," Computational Statistics & Data Analysis, Elsevier, vol. 147(C).

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    More about this item

    Keywords

    goodness-of-match; LASSO; ordinary least-squares estimation; portfolio tracking; representative portfolio; sample quantile;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • E6 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook

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