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Cross Validated SNP Density Estimates

  • Coppejans, Mark
  • Gallant, A. Ronald

We consider cross-validation strategies for the SNP nonparametric density estimator, which is a truncation (or sieve) estimator based upon a Hermite series expansion. Our main focus is on the use of SNP density estimators as an adjunct to EMM structural estimation. It is known that for this purpose a desirable truncation point occurs at the last point at which the MSE curve of the SNP density estimate declines abruptly. We study the determination of the MSE curve on a per sample basis for iid data by means of leave-one-out cross-validation and hold-out-sample cross-validation through an examination of their performance over the Marron-Wand test suite and models related to asset pricing and auction applications. We find that both methods are informative as to the location of abrupt drops. The hold-out-sample method is cheaper to compute because it requires fewer nonlinear optimizations. The minimum of the hold-out-sample cross-validation curve also seems to be a better indicator of the minimum of the true MSE curve. We consider the asymptotic justification of hold-out-sample cross-validation. For this purpose, we establish rates of convergence of the SNP estimator under the Hellinger norm that are of interest in their own right.

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Paper provided by Duke University, Department of Economics in its series Working Papers with number 00-10.

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Date of creation: 2000
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Handle: RePEc:duk:dukeec:00-10
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  1. A. Ronald Gallant & Chien-Te Hsu & George Tauchen, 1999. "Using Daily Range Data To Calibrate Volatility Diffusions And Extract The Forward Integrated Variance," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 617-631, November.
  2. Alexander Michaelides & Serena Ng, 1997. "Estimating the Rational Expectations Model of Speculative Storage: A Monte Carlo Comparison of Three Simulation Estimators," Boston College Working Papers in Economics 373, Boston College Department of Economics.
  3. Andersen, Torben G. & Chung, Hyung-Jin & Sorensen, Bent E., 1999. "Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 91(1), pages 61-87, July.
  4. Ronald Gallant, A. & Tauchen, George, 1999. "The relative efficiency of method of moments estimators1," Journal of Econometrics, Elsevier, vol. 92(1), pages 149-172, September.
  5. Eastwood, Brian J. & Gallant, A. Ronald, 1991. "Adaptive Rules for Seminonparametric Estimators That Achieve Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 7(03), pages 307-340, September.
  6. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  7. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
  8. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  9. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
  10. Laffont & Ossard & Vuong, 1995. "Econometrics of first-price auctions," Working Papers 153731, Institut National de la Recherche Agronomique, France.
  11. Gallant, A.R. & Tauchen, G., 1988. "Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Papers 88-59, Chicago - Graduate School of Business.
  12. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
  13. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
  14. Romulo Chumacero, . "Finite Sample Properties of the Efficient Method of Moments," Computing in Economics and Finance 1997 5, Society for Computational Economics.
  15. Fenton, Victor M. & Gallant, A. Ronald, 1996. "Qualitative and asymptotic performance of SNP density estimators," Journal of Econometrics, Elsevier, vol. 74(1), pages 77-118, September.
  16. Gallant, A. Ronald & Souza, Geraldo, 1991. "On the asymptotic normality of Fourier flexible form estimates," Journal of Econometrics, Elsevier, vol. 50(3), pages 329-353, December.
  17. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
  18. Liu, Ming, 2000. "Modeling long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 99(1), pages 139-171, November.
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