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Quantile-Based Inference for Tempered Stable Distributions

Author

Listed:
  • Hasan A. Fallahgoul

    (Monash University)

  • David Veredas

    (Vlerick Business School
    University of Ghent)

  • Frank J. Fabozzi

    (EDHEC Business School)

Abstract

We introduce a simple, fast, and accurate way for the estimation of numerous distributions that belong to the class of tempered stable probability distributions. Estimation is based on the method of simulated quantiles (Dominicy and Veredas in J Econom 172:235–247, 2013). MSQ consists of matching empirical and theoretical functions of quantiles that are informative about the parameters of interest. In the Monte Carlo study we show that MSQ is significantly faster than maximum likelihood and the MSQ estimators can be nearly as precise as MLE’s. A Value at Risk study using 13 years of daily returns from 21 world-wide market indexes shows that the risk assessments of MSQ estimates are as good as MLE’s.

Suggested Citation

  • Hasan A. Fallahgoul & David Veredas & Frank J. Fabozzi, 2019. "Quantile-Based Inference for Tempered Stable Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 51-83, January.
    • Handle: RePEc:kap:compec:v:53:y:2019:i:1:d:10.1007_s10614-017-9718-0
    DOI: 10.1007/s10614-017-9718-0
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    References listed on IDEAS

    as
    1. Hassan A. Fallahgoul & Young S. Kim & Frank J. Fabozzi, 2016. "Elliptical tempered stable distribution," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1069-1087, July.
    2. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    3. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    4. Jimmie Goode & Kim & Fabozzi, 2015. "Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations," Applied Economics, Taylor & Francis Journals, vol. 47(48), pages 5147-5158, October.
    5. Neil Shephard & Ole E. Barndorff-Nielsen & University of Aarhus, 2001. "Normal Modified Stable Processes," Economics Series Working Papers 72, University of Oxford, Department of Economics.
    6. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Mitov, Ivan & Fabozzi, Frank J., 2011. "Time series analysis for financial market meltdowns," Journal of Banking & Finance, Elsevier, vol. 35(8), pages 1879-1891, August.
    7. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(6), pages 797-834, December.
    8. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    9. Zhao, Zhibiao & Xiao, Zhijie, 2014. "Efficient Regressions Via Optimally Combining Quantile Information," Econometric Theory, Cambridge University Press, vol. 30(6), pages 1272-1314, December.
    10. Menn, Christian & Rachev, Svetlozar T., 2006. "Calibrated FFT-based density approximations for [alpha]-stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 1891-1904, April.
    11. Young Kim & Rosella Giacometti & Svetlozar Rachev & Frank Fabozzi & Domenico Mignacca, 2012. "Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model," Annals of Operations Research, Springer, vol. 201(1), pages 325-343, December.
    12. repec:ulb:ulbeco:2013/136280 is not listed on IDEAS
    13. Dominicy, Yves & Veredas, David, 2013. "The method of simulated quantiles," Journal of Econometrics, Elsevier, vol. 172(2), pages 235-247.
    14. Gajda, Janusz & Wyłomańska, Agnieszka, 2013. "Tempered stable Lévy motion driven by stable subordinator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(15), pages 3168-3176.
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    Cited by:

    1. Aubain Nzokem & Daniel Maposa, 2024. "Fitting the Seven-Parameter Generalized Tempered Stable Distribution to Financial Data," JRFM, MDPI, vol. 17(12), pages 1-29, November.
    2. Hasan Fallahgoul & Gregoire Loeper, 2021. "Modelling tail risk with tempered stable distributions: an overview," Annals of Operations Research, Springer, vol. 299(1), pages 1253-1280, April.

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    More about this item

    Keywords

    Heavy tailed distribution; Tempered stable distribution; Method of simulated quantiles;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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