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Testing the assumptions behind importance sampling

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Author Info

  • Koopman, Siem Jan
  • Shephard, Neil
  • Creal, Drew

Abstract

Importance sampling is used in many areas of modern econometrics to approximate unsolvable integrals. Its reliable use requires the sampler to possess a variance, for this guarantees a square root speed of convergence and asymptotic normality of the estimator of the integral. However, this assumption is seldom checked. In this paper we use extreme value theory to empirically assess the appropriateness of this assumption. Our main application is the stochastic volatility model, where importance sampling is commonly used for maximum likelihood estimation of the parameters of the model.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 149 (2009)
Issue (Month): 1 (April)
Pages: 2-11

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Handle: RePEc:eee:econom:v:149:y:2009:i:1:p:2-11

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Extreme value theory Importance sampling Simulation Stochastic volatility;

References

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  1. Elerian, O. & Chib, S. & Shephard, N., 1998. "Likelihood INference for Discretely Observed Non-linear Diffusions," Economics Papers 146, Economics Group, Nuffield College, University of Oxford.
  2. Sungbae An & Frank Schorfheide, 2006. "Bayesian analysis of DSGE models," Working Papers 06-5, Federal Reserve Bank of Philadelphia.
  3. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
  4. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Papers 321, University of Pittsburgh, Department of Economics, revised Jan 2007.
  5. Brandt, Michael W. & Kang, Qiang, 2004. "On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach," Journal of Financial Economics, Elsevier, vol. 72(2), pages 217-257, May.
  6. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
  7. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
  8. Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September.
  9. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1981. "Kuhn-Tucker, likelihood ratio and Wald tests for nonlinear models with inequality constraints on the parameters," Journal of Econometrics, Elsevier, vol. 16(1), pages 166-166, May.
  10. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
  11. Borus Jungbacker & Siem Jan Koopman, 2007. "Monte Carlo Estimation for Nonlinear Non-Gaussian State Space Models," Biometrika, Biometrika Trust, vol. 94(4), pages 827-839.
  12. Manabu Asai & Michael McAleer, 2006. "Asymmetric Multivariate Stochastic Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 453-473.
  13. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  14. Jesus Gonzalo, 2004. "Which Extreme Values Are Really Extreme?," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(3), pages 349-369.
  15. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  16. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  17. Durham, Garland B., 2006. "Monte Carlo methods for estimating, smoothing, and filtering one- and two-factor stochastic volatility models," Journal of Econometrics, Elsevier, vol. 133(1), pages 273-305, July.
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Citations

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Cited by:
  1. Geert Mesters & Siem Jan Koopman, 2012. "A Forty Year Assessment of Forecasting the Boat Race," Tinbergen Institute Discussion Papers 12-110/III, Tinbergen Institute.
  2. Siem Jan Koopman & Rutger Lit, 2012. "A Dynamic Bivariate Poisson Model for Analysing and Forecasting Match Results in the English Premier League," Tinbergen Institute Discussion Papers 12-099/III, Tinbergen Institute.
  3. Mesters, G. & Koopman, S.J., 2014. "Generalized dynamic panel data models with random effects for cross-section and time," Journal of Econometrics, Elsevier, vol. 180(2), pages 127-140.
  4. Siem Jan Koopman & Andre Lucas & Marcel Scharth, 2011. "Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models," Tinbergen Institute Discussion Papers 11-057/4, Tinbergen Institute, revised 27 Jan 2012.
  5. Geert Mesters & Siem Jan Koopman & Marius Ooms, 2011. "Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models," Tinbergen Institute Discussion Papers 11-090/4, Tinbergen Institute.
  6. Siem Jan Koopman & Rutger Lit & Andr� Lucas, 2014. "The Dynamic Skellam Model with Applications," Tinbergen Institute Discussion Papers 14-032/IV/DSF73, Tinbergen Institute.
  7. Charles S. Bos, 2011. "Relating Stochastic Volatility Estimation Methods," Tinbergen Institute Discussion Papers 11-049/4, Tinbergen Institute.
  8. Geert Mesters & Siem Jan Koopman, 2012. "Generalized Dynamic Panel Data Models with Random Effects for Cross-Section and Time," Tinbergen Institute Discussion Papers 12-009/4, Tinbergen Institute, revised 18 Mar 2014.
  9. Siem Jan Koopman & and Geert Mesters, 2014. "Empirical Bayes Methods for Dynamic Factor Models," Tinbergen Institute Discussion Papers 14-061/III, Tinbergen Institute.
  10. Wu, Xin-Yu & Ma, Chao-Qun & Wang, Shou-Yang, 2012. "Warrant pricing under GARCH diffusion model," Economic Modelling, Elsevier, vol. 29(6), pages 2237-2244.
  11. Pastorello, S. & Rossi, E., 2010. "Efficient importance sampling maximum likelihood estimation of stochastic differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2753-2762, November.
  12. Chao Huang & Jin-Guan Lin & Yan-Yan Ren, 2013. "Testing for the shape parameter of generalized extreme value distribution based on the $$L_q$$ -likelihood ratio statistic," Metrika, Springer, vol. 76(5), pages 641-671, July.
  13. Christian Brinch, 2012. "Efficient simulated maximum likelihood estimation through explicitly parameter dependent importance sampling," Computational Statistics, Springer, vol. 27(1), pages 13-28, March.
  14. Geert Mesters & Siem Jan Koopman, 2012. "A Forty Year Assessment of Forecasting the Boat Race," Tinbergen Institute Discussion Papers 12-110/III, Tinbergen Institute.
  15. Tore Selland Kleppe & Jun Yu & Hans J. skaug, 2011. "Simulated Maximum Likelihood Estimation for Latent Diffusion Models," Working Papers 10-2011, Singapore Management University, School of Economics.
  16. Edward P. Herbst & Frank Schorfheide, 2013. "Sequential Monte Carlo Sampling for DSGE Models," NBER Working Papers 19152, National Bureau of Economic Research, Inc.
  17. Geert Mesters & Siem Jan Koopman & Marius Ooms, 2011. "Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models," Tinbergen Institute Discussion Papers 11-090/4, Tinbergen Institute.
  18. Geert Mesters & Siem Jan Koopman, 2012. "Generalized Dynamic Panel Data Models with Random Effects for Cross-Section and Time," Tinbergen Institute Discussion Papers 12-009/4, Tinbergen Institute, revised 18 Mar 2014.
  19. Siem Jan Koopman & Rutger Lit, 2012. "A Dynamic Bivariate Poisson Model for Analysing and Forecasting Match Results in the English Premier League," Tinbergen Institute Discussion Papers 12-099/III, Tinbergen Institute.

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