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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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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 110 (2002)
Issue (Month): 1 (September)
Pages: 27-65

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Handle: RePEc:eee:econom:v:110:y:2002:i:1:p:27-65
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  1. Victor Fenton & Gallant, A. Ronald, 1996. "Qualitative and Asymptotic Performance of SNP Density Estimators," Working Papers 96-17, Duke University, Department of Economics.
  2. Laffont, Jean-Jacques & Ossard, Hervé & Vuong, Quang, 1991. "Econometrics of First-Price Auctions," IDEI Working Papers 7, Institut d'Économie Industrielle (IDEI), Toulouse.
  3. GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Gallant, A.R. & Tauchen, G., 1988. "Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Papers 88-59, Chicago - Graduate School of Business.
  5. 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.
  6. Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002. "Alternative Models for Stock Price Dynamics," CIRANO Working Papers 2002s-58, CIRANO.
  7. Michaelides, Alexander & Ng, Serena, 2000. "Estimating the rational expectations model of speculative storage: A Monte Carlo comparison of three simulation estimators," Journal of Econometrics, Elsevier, vol. 96(2), pages 231-266, June.
  8. Gallant, A. Ronald & Hsu, Chien-Te & Tauchen, George, 2000. "Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance," Working Papers 00-04, Duke University, Department of Economics.
  9. 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.
  10. 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.
  11. Chumacero Rómulo A., 1997. "Finite Sample Properties of the Efficient Method of Moments," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(2), pages 1-19, July.
  12. 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.
  13. 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.
  14. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
  15. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
  16. Liu, Ming, 2000. "Modeling long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 99(1), pages 139-171, November.
  17. 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.
  18. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
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