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Testing the Assumptions Behind the Use of Importance Sampling

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Abstract

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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File URL: http://www.nuff.ox.ac.uk/economics/papers/2002/w17/isdiagwp.pdf
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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2002-W17.

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Length: 14 pages
Date of creation: 01 Jun 2002
Date of revision:
Handle: RePEc:nuf:econwp:0217

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Web page: http://www.nuff.ox.ac.uk/economics/

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

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  1. Andersen, Torben G., 2000. "Simulation-Based Econometric Methods," Econometric Theory, Cambridge University Press, vol. 16(01), pages 131-138, February.
  2. 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.
  3. Tripathi, Gautam, 2000. "Econometric Methods," Econometric Theory, Cambridge University Press, vol. 16(01), pages 139-142, February.
  4. GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. 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.
  6. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
  7. Hajivassiliou, Vassilis A & Ruud, Paul A., 1993. "Classical Estimation Methods for LDV Models Using Simulation," Department of Economics, Working Paper Series qt3cg196fr, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  8. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  9. 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.
  10. Neil Shephard & Michael K Pitt, 1995. "Likelihood analysis of non-Gaussian parameter driven models," Economics Papers 15 & 108., Economics Group, Nuffield College, University of Oxford.
  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. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, Spring.
  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. 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.
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Cited by:
  1. Jean-Francois Richard & Roman Liesenfeld, 2007. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Working Papers 322, University of Pittsburgh, Department of Economics, revised Jan 2004.
  2. Liesenfeld, Roman & Richard, Jean-François, 2006. "Improving MCMC Using Efficient Importance Sampling," Economics Working Papers 2006,05, Christian-Albrechts-University of Kiel, Department of Economics.
  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. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
  5. Siem Jan Koopman & Kai Ming Lee, 2005. "Measuring Asymmetric Stochastic Cycle Components in U.S. Macroeconomic Time Series," Tinbergen Institute Discussion Papers 05-081/4, Tinbergen Institute.
  6. 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.

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