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Testing the assumptions behind importance sampling

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  • 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. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
  2. Manabu Asai & Michael McAleer, 2005. "Asymmetric Multivariate Stochastic Volatility," DEA Working Papers 12, Universitat de les Illes Balears, Departament d'Economía Aplicada.
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  8. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Papers 321, University of Pittsburgh, Department of Economics, revised Jan 2007.
  9. Durham, Garland B., 2003. "Likelihood-based specification analysis of continuous-time models of the short-term interest rate," Journal of Financial Economics, Elsevier, vol. 70(3), pages 463-487, December.
  10. GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Jesus Gonzalo, 2004. "Which Extreme Values Are Really Extreme?," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(3), pages 349-369.
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  13. Sungbae An & Frank Schorfheide, 2006. "Bayesian analysis of DSGE models," Working Papers 06-5, Federal Reserve Bank of Philadelphia.
  14. Danielsson, J & Richard, J-F, 1993. "Accelerated Gaussian Importance Sampler with Application to Dynamic Latent Variable Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S153-73, Suppl. De.
  15. 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.
  16. 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.
  17. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
  18. 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.
  19. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
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Citations

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Cited by:
  1. 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.
  2. Geert Mesters & Siem Jan Koopman, 2012. "A Forty Year Assessment of Forecasting the Boat Race," Tinbergen Institute Discussion Papers 12-110/III, Tinbergen Institute.
  3. 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.
  4. Charles S. Bos, 2011. "Relating Stochastic Volatility Estimation Methods," Tinbergen Institute Discussion Papers 11-049/4, Tinbergen Institute.
  5. Edward P. Herbst & Frank Schorfheide, 2013. "Sequential Monte Carlo sampling for DSGE models," Finance and Economics Discussion Series 2013-43, Board of Governors of the Federal Reserve System (U.S.).
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Tore Selland Kleppe & Jun Yu & Hans J. Skaug, 2012. "Simulated Maximum Likelihood Estimation for Latent Diffusion Models," Working Papers 12-2012, Singapore Management University, School of Economics.
  12. Christian Brinch, 2012. "Efficient simulated maximum likelihood estimation through explicitly parameter dependent importance sampling," Computational Statistics, Springer, vol. 27(1), pages 13-28, March.
  13. 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.
  14. Siem Jan Koopman & Rutger Lit & André Lucas, 2014. "The Dynamic Skellam Model with Applications," Tinbergen Institute Discussion Papers 14-032/IV/DSF73, Tinbergen Institute.
  15. 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.
  16. 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.
  17. Geert Mesters & Siem Jan Koopman, 2012. "A Forty Year Assessment of Forecasting the Boat Race," Tinbergen Institute Discussion Papers 12-110/III, Tinbergen Institute.
  18. 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.
  19. Siem Jan Koopman & Geert Mesters, 2014. "Empirical Bayes Methods for Dynamic Factor Models," Tinbergen Institute Discussion Papers 14-061/III, Tinbergen Institute.

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