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The method of simulated quantiles

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  • Yves Dominicy
  • David Veredas

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.

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Bibliographic Info

Paper provided by ULB -- Universite Libre de Bruxelles in its series ULB Institutional Repository with number 2013/136280.

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Date of creation: 2013
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Publication status: Published in: Journal of econometrics (2013) v.172 n° 2,p.235-247
Handle: RePEc:ulb:ulbeco:2013/136280

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References

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  1. Daniel McFadden, 1987. "A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration," Working papers 464, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, October.
  3. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
  4. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  5. Garcia, René & Renault, Eric & Veredas, David, 2011. "Estimation of stable distributions by indirect inference," Journal of Econometrics, Elsevier, vol. 161(2), pages 325-337, April.
  6. Marco J. Lombardi, 2004. "Bayesian inference for alpha-stable distributions: a random walk MCMC approach," Econometrics Working Papers Archive wp2004_11, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  7. Carrasco, Marine & Florens, Jean-Pierre, 2002. "Efficient GMM Estimation Using the Empirical Characteristic Function," IDEI Working Papers 140, Institut d'Économie Industrielle (IDEI), Toulouse.
  8. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-52, July.
  9. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
  10. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2000. "Diagnosing and treating the fat tails in financial returns data," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 389-416, November.
  11. Ghose, Devajyoti & Kroner, Kenneth F., 1995. "The relationship between GARCH and symmetric stable processes: Finding the source of fat tails in financial data," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 225-251, September.
  12. de Vries, Casper G., 1991. "On the relation between GARCH and stable processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 313-324, June.
  13. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De.
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Cited by:
  1. Borak, Szymon & Misiorek, Adam & Weron, Rafal, 2010. "Models for Heavy-tailed Asset Returns," MPRA Paper 25494, University Library of Munich, Germany.
  2. Wojciech Charemza & Carlos Diaz Vela & Svetlana Makarova, 2013. "Too many skew normal distributions? The practitioner’s perspective," Discussion Papers in Economics 13/07, Department of Economics, University of Leicester.
  3. 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.
  4. Yves Dominicy & Hiroaki Ogata & David Veredas, 2013. "Inference for vast dimensional elliptical distributions," Computational Statistics, Springer, vol. 28(4), pages 1853-1880, August.
  5. Wojciech Charemza & Carlos Diaz Vela & Svetlana Makarova, 2013. "Inflation fan charts, monetary policy and skew normal distribution," Discussion Papers in Economics 13/06, Department of Economics, University of Leicester.
  6. 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.
  7. Matteo Barigozzi & Roxana Halbleib & David Veredas, 2012. "Which model to match?," Banco de Espa�a Working Papers 1229, Banco de Espa�a.
  8. 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.
  9. Wojciech Charemza & Carlos Diaz & Svetlana Makarova, 2014. "Term Structure Of Inflation Forecast Uncertainties And Skew Normal Distributions," Discussion Papers in Economics 14/01, Department of Economics, University of Leicester.
  10. Ogata, Hiroaki, 2013. "Estimation for multivariate stable distributions with generalized empirical likelihood," Journal of Econometrics, Elsevier, vol. 172(2), pages 248-254.
  11. Adam Misiorek & Rafal Weron, 2010. "Heavy-tailed distributions in VaR calculations," HSC Research Reports HSC/10/05, Hugo Steinhaus Center, Wroclaw University of Technology.

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