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A Test for Comparing Multiple Misspecified Conditional Distributions

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Author Info
Valentina Corradi () (Queen Mary, University of London)
Norman R. Swanson () (Rutgers University)

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Abstract

This paper introduces a conditional Kolmogorov test, in the spirit of Andrews (1997), that allows for comparison of multiple misspecifed conditional distribution models, for the case of dependent observations. A conditional confidence interval version of the test is also discussed. Model accuracy is measured using a distributional analog of mean square error, in which the squared (approximation) error associated with a given model, say model i; is measured in terms of the average over U of E((Fi(u|Zt,Theta-t-plus)-Fo(u|Zt,Theta-o)))^2; where U is a possibly unbounded set on the real line, Zt is the conditioning information set, Fi is the distribution function of a particular candidate model, and F0 is the true (unkown) distribution function. When comparing more than two models, a “benchmark” model is specified, and the test is constructed along the lines of the “reality check” of White (2000). Valid asymptotic critical values are obtained via a version of the block bootstrap which properly captures the e®ect of parameter estimation error. The results of a small Monte Carlo experiment indicate that the conditional confidence interval version of the test has reasonable finite sample properties even for samples with as few as 60 observations.

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Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 200314.

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Date of creation: 21 Oct 2003
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Handle: RePEc:rut:rutres:200314

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Related research
Keywords: block bootstrap; conditional Kolmogorov test; data snooping; misspecified conditional distribution;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  4. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-35, April.
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  6. Peter F. Christoffersen & Francis X. Diebold, 2000. "How Relevant is Volatility Forecasting for Financial Risk Management?," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 12-22, February. [Downloadable!] (restricted)
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  7. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
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  11. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
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  12. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March. [Downloadable!] (restricted)
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  16. Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, vol. 98(1), pages 27-46, September. [Downloadable!] (restricted)
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  19. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October. [Downloadable!] (restricted)
  20. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
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  22. Valentina Corradi & Norman R. Swanson, 2003. "Bootstrap Conditional Distribution Tests In the Presence of Dynamic Misspecification," Departmental Working Papers 200311, Rutgers University, Department of Economics. [Downloadable!]
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  23. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January. [Downloadable!] (restricted)
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  25. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," Review of Economic Studies, Blackwell Publishing, vol. 72(3), pages 735-765, 07. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Valentina Corradi & Norman R. Swanson, 2003. "Evaluation of Dynamic Stochastic General Equilibrium Models Based on Distributional Comparison of Simulated and Historical Data," Departmental Working Papers 200320, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  2. Gianni Amisano & Raffaella Giacomini, 2005. "Comparing Density Forecsts via Weighted Likelihood Ratio Tests," Working Papers ubs0504, University of Brescia, Department of Economics. [Downloadable!]
    Other versions:
  3. Valentina Corradi & Norman Swanson & Geetesh Bhardwaj, 2006. "A Simulation Based Specification Test for Diffusion Processes," Departmental Working Papers 200614, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  4. Valentina Corradi & Norman Swanson, 2004. "Predective Density and Conditional Confidence Interval Accuracy Tests," Departmental Working Papers 200423, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  5. Valentina Corradi & Norman Swanson, 2003. "The Block Bootstrap for Parameter Estimation Error In Recursive Estimation Schemes, With Applications to Predictive Evaluation," Departmental Working Papers 200313, Rutgers University, Department of Economics. [Downloadable!]
  6. Michael P. Clements & Philip Hans Franses & Norman R. Swanson, 2003. "Forecasting economic and financial time-series with non-linear models," Departmental Working Papers 200309, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  7. Xiaohong Chen & Yanqin Fan, 2004. "Estimation and Model Selection of Semiparametric Copula-Based Multivariate Dynamic Models under Copula Misspecification," Working Papers 0419, Department of Economics, Vanderbilt University, revised Sep 2004. [Downloadable!]
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