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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.

Suggested Citation

  • Koopman, Siem Jan & Shephard, Neil & Creal, Drew, 2009. "Testing the assumptions behind importance sampling," Journal of Econometrics, Elsevier, vol. 149(1), pages 2-11, April.
    • Handle: RePEc:eee:econom:v:149:y:2009:i:1:p:2-11
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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
    3. 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.
    4. Manabu Asai & Michael McAleer, 2006. "Asymmetric Multivariate Stochastic Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 453-473.
    5. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    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. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    8. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
    9. H. Kahn & A. W. Marshall, 1953. "Methods of Reducing Sample Size in Monte Carlo Computations," Operations Research, INFORMS, vol. 1(5), pages 263-278, November.
    10. 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 153-173, Suppl. De.
    11. 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.
    12. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 297-316, July.
    13. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 335-338, July.
    14. Jesus Gonzalo, 2004. "Which Extreme Values Are Really Extreme?," Journal of Financial Econometrics, Oxford University Press, vol. 2(3), pages 349-369.
    15. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
    16. 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.
    17. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-993, July.
    23. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Paper 321, Department of Economics, University of Pittsburgh, revised Jan 2007.
    24. 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.
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    Cited by:

    1. Mengheng Li & Siem Jan (S.J.) Koopman, 2018. "Unobserved Components with Stochastic Volatility in U.S. Inflation: Estimation and Signal Extraction," Tinbergen Institute Discussion Papers 18-027/III, Tinbergen Institute.
    2. Dominik Bertsche & Robin Braun, 2022. "Identification of Structural Vector Autoregressions by Stochastic Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 328-341, January.
    3. Arias, Jonas E. & Rubio-Ramírez, Juan F. & Waggoner, Daniel F., 2021. "Inference in Bayesian Proxy-SVARs," Journal of Econometrics, Elsevier, vol. 225(1), pages 88-106.
    4. G. Mesters & S. J. Koopman & M. Ooms, 2016. "Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 659-687, April.
    5. Siem Jan Koopman & Rutger Lit & André Lucas, 2017. "Intraday Stochastic Volatility in Discrete Price Changes: The Dynamic Skellam Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1490-1503, October.
    6. 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.
    7. Charles S. Bos, 2011. "Relating Stochastic Volatility Estimation Methods," Tinbergen Institute Discussion Papers 11-049/4, Tinbergen Institute.
    8. Youngjun Choe & Henry Lam & Eunshin Byon, 2018. "Uncertainty Quantification of Stochastic Simulation for Black-box Computer Experiments," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1155-1172, December.
    9. 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.
    10. Mao, Xiuping & Czellar, Veronika & Ruiz, Esther & Veiga, Helena, 2020. "Asymmetric stochastic volatility models: Properties and particle filter-based simulated maximum likelihood estimation," Econometrics and Statistics, Elsevier, vol. 13(C), pages 84-105.
    11. Siem Jan Koopman & Rutger Lit & André Lucas, 2014. "The Dynamic Skellam Model with Applications," Tinbergen Institute Discussion Papers 14-032/IV/DSF73, Tinbergen Institute, revised 06 Jul 2015.
    12. S. J. Koopman & G. Mesters, 2017. "Empirical Bayes Methods for Dynamic Factor Models," The Review of Economics and Statistics, MIT Press, vol. 99(3), pages 486-498, July.
    13. Bräuning, Falk & Koopman, Siem Jan, 2020. "The dynamic factor network model with an application to international trade," Journal of Econometrics, Elsevier, vol. 216(2), pages 494-515.
    14. Scharth, Marcel & Kohn, Robert, 2016. "Particle efficient importance sampling," Journal of Econometrics, Elsevier, vol. 190(1), pages 133-147.
    15. Kleppe, Tore Selland & Yu, Jun & Skaug, Hans J., 2014. "Maximum likelihood estimation of partially observed diffusion models," Journal of Econometrics, Elsevier, vol. 180(1), pages 73-80.
    16. 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.
    17. Siem Jan Koopman & Rutger Lit, 2015. "A dynamic bivariate Poisson model for analysing and forecasting match results in the English Premier League," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(1), pages 167-186, January.
    18. 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: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 641-671, July.
    19. Falk Bräuning & Siem Jan Koopman, 2016. "The dynamic factor network model with an application to global credit risk," Working Papers 16-13, Federal Reserve Bank of Boston.
    20. 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.
    21. Mengheng Li & Siem Jan Koopman, 2021. "Unobserved components with stochastic volatility: Simulation‐based estimation and signal extraction," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 614-627, August.
    22. Matti Vihola & Jouni Helske & Jordan Franks, 2020. "Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1339-1376, December.
    23. Siem Jan Koopman & André Lucas & Marcel Scharth, 2015. "Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State-Space Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 114-127, January.
    24. Christian Brinch, 2012. "Efficient simulated maximum likelihood estimation through explicitly parameter dependent importance sampling," Computational Statistics, Springer, vol. 27(1), pages 13-28, March.
    25. Edward Herbst & Frank Schorfheide, 2014. "Sequential Monte Carlo Sampling For Dsge Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1073-1098, November.

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