Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T18:23:29.341Z Has data issue: false hasContentIssue false
  • English
  • Français

A TEST FOR COMPARING MULTIPLE MISSPECIFIED CONDITIONAL INTERVAL MODELS

Published online by Cambridge University Press:  22 August 2005

Valentina Corradi  and
Norman R. Swanson
Valentina Corradi
Affiliation:
Queen Mary–University of London
Norman R. Swanson
Affiliation:
Rutgers University
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper introduces a test for the comparison of multiple misspecified conditional interval models, for the case of dependent observations. Model accuracy is measured using a distributional analog of mean square error, in which the approximation error associated with a given model, say, model i, for a given interval, is measured by the expected squared difference between the conditional confidence interval under model i and the “true” one.

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, Econometrica 68, 1097–1126). Valid asymptotic critical values are obtained via a version of the block bootstrap that properly captures the effect of parameter estimation error. The results of a small Monte Carlo experiment indicate that the test does not have unreasonable finite sample properties, given small samples of 60 and 120 observations, although the results do suggest that larger samples should likely be used in empirical applications of the test.The authors express their gratitude to Don Andrews and an anonymous referee for providing numerous useful suggestions, all of which we feel have been instrumental in improving earlier drafts of this paper. The authors also thank Russell Davidson, Clive Granger, Lutz Kilian, Christelle Viaroux, and seminar participants at the 2002 UK Econometrics Group meeting in Bristol, the 2002 European Econometric Society meetings, the 2002 University of Pennsylvania NSF-NBER time series conference, the 2002 EC2 Conference in Bologna, Cornell University, the State University of New York at Stony Brook, and the University of California at Davis for many helpful comments and suggestions on previous versions of this paper.

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 5 , October 2005 , pp. 991 - 1016
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Altissimo, F. & A. Mele (2002) Testing the Closeness of Conditional Densities by Simulated Nonparametric Methods. Working paper, LSE.
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858.Google Scholar
Andrews, D.W.K. (1997) A conditional Kolmogorov test. Econometrica 65, 1097–1128.Google Scholar
Andrews, D.W.K. (2002) Higher-order improvements of a computationally attractive k-step bootstrap for extremum estimators. Econometrica 70, 119–162.Google Scholar
Bai, J. (2003) Testing parametric conditional distributions of dynamic models. Review of Economics and Statistics 85, 531–549.Google Scholar
Benjamini, Y. & Y. Hochberg (1995) Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, series B 57, 289–300.Google Scholar
Chang, Y.S., J.F. Gomes, & F. Schorfheide (2002) Learning-by-doing as a propagation mechanism. American Economic Review 92, 1498–1520.Google Scholar
Chatfield, C. (1993) Calculating interval forecasts. Journal of Business & Economic Statistics 11, 121–135.Google Scholar
Christoffersen, P.F. (1998) Evaluating interval forecasts. International Economic Review 39, 841–862.Google Scholar
Christoffersen, P. & F.X. Diebold (2000) How relevant is volatility forecasting for financial risk management? Review of Economics and Statistics 82, 12–22.Google Scholar
Clements, M.P. & N. Taylor (2001) Bootstrapping prediction intervals for autoregressive models. International Journal of Forecasting 17, 247–276.Google Scholar
Corradi, V. & N.R. Swanson (2004a) Bootstrap Procedures for Recursive Estimation Schemes with Application to Forecast Model Selection. Working paper, Rutgers University.
Corradi, V. & N.R. Swanson (2004b) Predictive Density Accuracy Tests. Working paper, Rutgers University.
Corradi, V. & N.R. Swanson (2005a) Bootstrap conditional distribution tests in the presence of dynamic misspecification. Journal of Econometrics, forthcoming.Google Scholar
Corradi, V. & N.R. Swanson (2005b) Evaluation of dynamic stochastic general equilibrium models based on distributional comparison of simulated and historical data. Journal of Econometrics, forthcoming.Google Scholar
Diebold, F.X., T. Gunther, & A.S. Tay (1998) Evaluating density forecasts with applications to finance and management. International Economic Review 39, 863–883.Google Scholar
Diebold, F.X., J. Hahn, & A.S. Tay (1999) Multivariate density forecast evaluation and calibration in financial risk management: High frequency returns on foreign exchange. Review of Economics and Statistics 81, 661–673.Google Scholar
Diebold, F.X., A.S. Tay, & K.D. Wallis (1998) Evaluating Density Forecasts of Inflation: The Survey of Professional Forecasters. In R.F. Engle & H. White (eds.), Festschrift in Honor of C.W.J. Granger, pp. 76–90. Oxford University Press.
Duffie, D. & J. Pan (1997) An overview of value at risk. Journal of Derivatives 4, 7–49.Google Scholar
Fernandez-Villaverde, J. & J.F. Rubio-Ramirez (2004) Comparing dynamic equilibrium models to data. Journal of Econometrics 123, 153–180.Google Scholar
Gallant, A.R. & H. White (1988) A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models. Blackwell.
Giacomini, R. (2002) Comparing Density Forecasts via Weighted Likelihood Ratio Tests: Asymptotic and Bootstrap Methods. Working paper, University of California, San Diego.
Giacomini, R. & I. Komunjer (2005) Evaluation and combination of conditional quantile forecasts. Journal of Business and Economic Statistics, forthcoming.Google Scholar
Goncalves, S. & H. White (2002) The bootstrap of the mean for dependent and heterogeneous arrays. Econometric Theory 18, 1367–1384.Google Scholar
Goncalves, S. & H. White (2004) Maximum likelihood and the bootstrap for nonlinear dynamic models. Journal of Econometrics 119, 199–219.Google Scholar
Götze, F. & H.R. Künsch (1996) Second-order correctness of the blockwise bootstrap for stationary observations. Annals of Statistics 24, 1914–1933.Google Scholar
Granger, C.W.J., H. White, & M. Kamstra (1989) Interval forecasting—An analysis based upon ARCH-quantile estimators. Journal of Econometrics 40, 87–96.Google Scholar
Hall, P. & J.K. Horowitz (1996) Bootstrap critical values for tests based on generalized method of moments estimators. Econometrica 64, 891–916.Google Scholar
Hall, P., J.K. Horowitz, & N.J. Jing (1995) On blocking rules for the bootstrap with dependent data. Biometrika 82, 561–574.Google Scholar
Hall, A.R. & A. Inoue (2003) The large sample behavior of the generalized method of moments estimator in misspecified models. Journal of Econometrics 114, 361–394.Google Scholar
Hansen, P.R. (2005) An unbiased test for superior predictive ability. Journal of Business and Economic Statistics, forthcoming.Google Scholar
Hochberg, Y. (1988) A sharper Bonferroni procedure for multiple significance tests. Biometrika 75, 800–803.Google Scholar
Hong, Y. (2001) Evaluation of Out of Sample Probability Density Forecasts with Applications to S&P 500 Stock Prices. Working paper, Cornell University.
Hong, Y.M. & H. Li (2005) Out of sample performance of spot interest rate models. Review of Financial Studies 18, 37–84.Google Scholar
Inoue, A. & M. Shintani (2004) Bootstrapping GMM estimators for time series. Journal of Econometrics, forthcoming.Google Scholar
Kitamura, Y. (2002) Econometric Comparisons of Conditional Models. Working paper, University of Pennsylvania.
Künsch, H.R. (1989) The jackknife and the bootstrap for general stationary observations. Annals of Statistics 17, 1217–1241.Google Scholar
Lahiri, S.N. (2003) Resampling Methods for Dependent Data. Springer-Verlag.
Li, F. & G. Tkacz (2004) A consistent test for conditional density functions with time dependent data. Journal of Econometrics, forthcoming.Google Scholar
Linton, O., E. Maasoumi, & Y.J. Whang (2003) Consistent testing for stochastic dominance under general sampling schemes. Review of Economic Studies, forthcoming.Google Scholar
Politis, D.N., J.P. Romano, & M. Wolf (1999) Subsampling. Springer-Verlag.
Schorfheide, F. (2000) Loss function based evaluation of DSGE models. Journal of Applied Econometrics 15, 645–670.Google Scholar
Spanos, A. (1999) Probability Theory and Statistical Inference: Econometric Modelling with Observational Data. Cambridge University Press.
Vuong, Q. (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57, 307–333.Google Scholar
Whang, Y.J. (2000) Consistent bootstrap tests of parametric regression functions. Journal of Econometrics 15, 27–46.Google Scholar
Whang, Y.J. (2001) Consistent specification testing for conditional moment restrictions. Economics Letters 71, 299–306.Google Scholar
White, H. (1982) Maximum likelihood estimation of misspecified models. Econometrica 50, 1–25.Google Scholar
White, H. (2000) A reality check for data snooping. Econometrica 68, 1097–1126.Google Scholar
Zheng, J.X. (2000) A consistent test of conditional parametric distribution. Econometric Theory 16, 667–691.Google Scholar