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Testing the Assumptions Behind the Use of Importance Sampling

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Importance sampling is used in many aspects 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 propose to use extreme value theory to empirically assess the appropriateness of this assumption. We illustrate this method in the context of a maximum simulated likelihood analysis of the stochastic volatility model.

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  • Siem Jan Koopman & Neil Shephard, 2002. "Testing the Assumptions Behind the Use of Importance Sampling," Economics Papers 2002-W17, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:0217
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    Cited by:

    1. Roman Liesenfeld & Jean-Francois Richard, 2006. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 335-360.
    2. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Paper 321, Department of Economics, University of Pittsburgh, revised Jan 2007.
    3. Pierre Collin-Dufresne & Christopher S. Jones & Robert S. Goldstein, 2004. "Can Interest Rate Volatility be Extracted from the Cross Section of Bond Yields? An Investigation of Unspanned Stochastic Volatility," NBER Working Papers 10756, National Bureau of Economic Research, Inc.
    4. Siem Jan Koopman & Charles S. Bos, 2002. "Time Series Models with a Common Stochastic Variance for Analysing Economic Time Series," Tinbergen Institute Discussion Papers 02-113/4, Tinbergen Institute.
    5. Liesenfeld, Roman & Richard, Jean-François, 2008. "Improving MCMC, using efficient importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 272-288, December.
    6. Jean-Francois Richard & Roman Liesenfeld, 2007. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Working Paper 322, Department of Economics, University of Pittsburgh, revised Jan 2004.
    7. Siem Jan Koopman & John A. D. Aston, 2006. "A non-Gaussian generalization of the Airline model for robust seasonal adjustment," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(5), pages 325-349.

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    Keywords

    Extreme value theory; Importance sampling; Simulation; Stochastic Volatility.;
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