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The method of simulated quantiles

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  • Dominicy, Yves
  • Veredas, David

Abstract

We introduce the Method of Simulated Quantiles, or MSQ, an indirect inference method based on quantile matching that is useful for situations where the density function does not have a closed form and/or moments do not exist. Functions of theoretical quantiles, which depend on the parameters of the assumed probability law, are matched with the sample counterparts, which depend on the observations. Since the theoretical quantiles may not be available analytically, the optimization is based on simulations. We illustrate the method with the estimation of α-stable distributions. A thorough Monte Carlo study and an illustration to 22 financial indexes show the usefulness of MSQ.

Suggested Citation

  • Dominicy, Yves & Veredas, David, 2013. "The method of simulated quantiles," Journal of Econometrics, Elsevier, vol. 172(2), pages 235-247.
    • Handle: RePEc:eee:econom:v:172:y:2013:i:2:p:235-247
    DOI: 10.1016/j.jeconom.2012.08.010
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    Cited by:

    1. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    2. Christophe Ley & Anouk Neven, 2013. "Simple Le Cam Optimal Inference for the Tail Weight of Multivariate Student t Distributions: Testing Procedures and Estimation," Working Papers ECARES ECARES 2013-26, ULB -- Universite Libre de Bruxelles.
    3. Tsionas, Mike G., 2016. "Bayesian analysis of multivariate stable distributions using one-dimensional projections," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 185-193.
    4. Mohammad Mohammadi & Adel Mohammadpour & Hiroaki Ogata, 2015. "On estimating the tail index and the spectral measure of multivariate $$\alpha $$ α -stable distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 549-561, July.
    5. Amengual, Dante & Fiorentini, Gabriele & Sentana, Enrique, 2013. "Sequential estimation of shape parameters in multivariate dynamic models," Journal of Econometrics, Elsevier, vol. 177(2), pages 233-249.
    6. Jung, Jae Wook & Simonovska, Ina & Weinberger, Ariel, 2019. "Exporter heterogeneity and price discrimination: A quantitative view," Journal of International Economics, Elsevier, vol. 116(C), pages 103-124.
    7. Qin, Shanshan & Wu, Yuehua, 2020. "General matching quantiles M-estimation," Computational Statistics & Data Analysis, Elsevier, vol. 147(C).
    8. Lynda Khalaf & Beatriz Peraza López, 2020. "Simultaneous Indirect Inference, Impulse Responses and ARMA Models," Econometrics, MDPI, vol. 8(2), pages 1-26, April.
    9. Yves Dominicy & Hiroaki Ogata & David Veredas, 2013. "Inference for vast dimensional elliptical distributions," Computational Statistics, Springer, vol. 28(4), pages 1853-1880, August.
    10. Grabchak, Michael, 2021. "An exact method for simulating rapidly decreasing tempered stable distributions in the finite variation case," Statistics & Probability Letters, Elsevier, vol. 170(C).
    11. Svetlana Makarova, 2016. "ECB footprints on inflation forecast uncertainty," Bank of Estonia Working Papers wp2016-5, Bank of Estonia, revised 19 Jul 2016.
    12. M. Bee & J. Hambuckers & L. Trapin, 2019. "Estimating Value-at-Risk for the g-and-h distribution: an indirect inference approach," Quantitative Finance, Taylor & Francis Journals, vol. 19(8), pages 1255-1266, August.
    13. Hallin, Marc & Swan, Yvik & Verdebout, Thomas & Veredas, David, 2013. "One-step R-estimation in linear models with stable errors," Journal of Econometrics, Elsevier, vol. 172(2), pages 195-204.
    14. Jabłońska-Sabuka, Matylda & Teuerle, Marek & Wyłomańska, Agnieszka, 2017. "Bivariate sub-Gaussian model for stock index returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 628-637.
    15. Charemza, Wojciech & Díaz, Carlos & Makarova, Svetlana, 2019. "Quasi ex-ante inflation forecast uncertainty," International Journal of Forecasting, Elsevier, vol. 35(3), pages 994-1007.
    16. 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.
    17. 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.
    18. Calzolari, Giorgio & Halbleib, Roxana, 2018. "Estimating stable latent factor models by indirect inference," Journal of Econometrics, Elsevier, vol. 205(1), pages 280-301.
    19. Ogata, Hiroaki, 2013. "Estimation for multivariate stable distributions with generalized empirical likelihood," Journal of Econometrics, Elsevier, vol. 172(2), pages 248-254.
    20. Matteo Barigozzi & Roxana Halbleib & David Veredas, 2012. "Which model to match?," Working Papers 1229, Banco de España.
    21. Svetlana Makarova, 2018. "European Central Bank Footprints On Inflation Forecast Uncertainty," Economic Inquiry, Western Economic Association International, vol. 56(1), pages 637-652, January.
    22. Paola Stolfi & Mauro Bernardi & Lea Petrella, 2018. "The sparse method of simulated quantiles: An application to portfolio optimization," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 375-398, August.

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    More about this item

    Keywords

    Quantiles; Simulation; Matching; Inference;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy

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