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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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    Cited by:

    1. 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.
    2. Christian Brinch, 2012. "Efficient simulated maximum likelihood estimation through explicitly parameter dependent importance sampling," Computational Statistics, Springer, vol. 27(1), pages 13-28, March.
    3. 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.
    4. 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.
    5. 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.
    6. Falk Bräuning & Siem Jan Koopman, 2016. "The Dynamic Factor Network Model with an Application to Global Credit-Risk," Tinbergen Institute Discussion Papers 16-105/III, Tinbergen Institute.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Charles S. Bos, 2011. "Relating Stochastic Volatility Estimation Methods," Tinbergen Institute Discussion Papers 11-049/4, Tinbergen Institute.
    18. 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.
    19. 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.
    20. Scharth, Marcel & Kohn, Robert, 2016. "Particle efficient importance sampling," Journal of Econometrics, Elsevier, vol. 190(1), pages 133-147.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. 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.

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