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ON THE LACK OF POWER OF OMNIBUS SPECIFICATION TESTS

Published online by Cambridge University Press:  01 February 2009

J. Carlos Escanciano
J. Carlos Escanciano*
Affiliation:
Indiana University
*
*Address correspondence to Juan Carlos Escanciano, Department of Economics, Indiana University, 100 S. Woodlawn, Wylie Hall, Bloomington, IN 47405-7104, USA; e-mail: [email protected].
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Abstract

Designed to have power against all alternatives, omnibus consistent tests are the primary econometric tools for testing the correct specification of parametric conditional means when there is no information about the possible alternative. The main purpose of this paper is to show that, contrary to what is generally believed, omnibus specification tests only have substantial local power against alternatives in a finite-dimensional space (usually unknown to the researcher). We call such a space the principal space. We characterize and estimate the principal space for Cramér–von Mises tests. These results are some of the by-products of a detailed theoretical power analysis carried out in the paper. This investigation focuses on the class of the so-called integrated consistent tests under possibly heteroskedastic time series. A Monte Carlo experiment examines the finite-sample properties of tests and estimators of preferred alternatives. Finally, an application of our theory to test the martingale difference hypothesis of some exchange rates provides new information on the rejection of omnibus tests and illustrates our findings.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 1 , February 2009 , pp. 162 - 194
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

An, H.S. & Bing, C. (1991) A Kolmogorov–Smirnov type statistic with application to test for non-linearity in time series. International Statistical Review 59, 287–307.Google Scholar
Andrews, D.W.K. & Ploberger, W. (1994) Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62, 1383–1414.CrossRefGoogle Scholar
Bierens, H.J. (1982) Consistent model specification tests. Journal of Econometrics 20, 105–134.CrossRefGoogle Scholar
Bierens, H.J. (1984) Model specification testing of time series regressions. Journal of Econometrics 26, 323–353.CrossRefGoogle Scholar
Bierens, H.J. (1990) A consistent conditional moment test of functional form. Econometrica 58, 1443–1458.CrossRefGoogle Scholar
Bierens, H.J. & Ploberger, W. (1997) Asymptotic theory of integrated conditional moment test. Econometrica 65, 1129–1151.CrossRefGoogle Scholar
Boning, W.B. & Sowell, F. (1999) Optimality for the integrated conditional moment test. Econometric Theory 15, 710–718.CrossRefGoogle Scholar
Bosq, D. (2000) Linear Processes in Function Spaces. Theory and Applications. Lecture Notes in Statistics 149. Springer-Verlag.CrossRefGoogle Scholar
Carrasco, M., Florens, J.P. & Renault, E. (2007) Linear inverse problems in structural econometrics: Estimation based on spectral decomposition and regularization. In Heckmen, J.J. & Learner, E.E. (eds.), Handbook of Econometrics, vol. 6B, pp. 5633–5751. North-Holland.CrossRefGoogle Scholar
Chen, X. & White, H. (1996) Laws of large numbers for Hilbert space-valued mixingales with applications. Econometric Theory 12, 284–304.CrossRefGoogle Scholar
Chen, X. & White, H. (1998) Central limit and functional central limit theorems for Hilbert-valued dependent heterogeneous arrays with applications. Econometric Theory 14, 260–284.CrossRefGoogle Scholar
de Jong, R.M. (1996) The Bierens’ test under data dependence. Journal of Econometrics 72, 1–32.CrossRefGoogle Scholar
Domínguez, M.A. & Lobato, I.N. (2003) A consistent test for the martingale difference hypothesis. Econometric Reviews 22, 351–377.CrossRefGoogle Scholar
Domínguez, M.A. & Lobato, I.N. (2004) Consistent estimation of models defined by conditional moment restrictions. Econometrica 72, 1601–1615.CrossRefGoogle Scholar
Durbin, J. & Knott, M. (1972) Components of the Cramer–von Mises statistics, part I. Journal of the Royal Statistical Society, Series B 34, 290–307.Google Scholar
Escanciano, J.C. (2006a) Model checks using residual marked empirical processes. Statistica Sinica 17, 115–138.Google Scholar
Escanciano, J.C. (2006b) Goodness-of-fit tests for linear and non-linear time series models. Journal of the American Statistical Association 101, 531–541.CrossRefGoogle Scholar
Escanciano, J.C. (2006c) A consistent diagnostic test for regression models using projections. Econometric Theory 22, 1030–1051.CrossRefGoogle Scholar
Escanciano, J.C. & Mayoral, S. (2007) Data-Driven Smooth Tests for the Martingale Difference Hypothesis. Universidad de Navarra Working paper 01/07, University de Navarra.Google Scholar
Escanciano, J.C. & Velasco, C. (2006) Generalized spectral tests for the martingale difference hypothesis. Journal of Econometrics 134, 151–185.CrossRefGoogle Scholar
Fan, J. & Yao, Q. (2003) Nonlinear Time Series: Nonparametric and Parametric Methods. Springer- Verlag.CrossRefGoogle Scholar
Fan, Y. & Li, Q. (2000) Consistent model specification tests: Kernel-based tests versus Bierens’ ICM tests. Econometric Theory 16, 1016–1041.CrossRefGoogle Scholar
Grenander, U. (1952) Stochastic processes and statistical inference. Arkiv för Matematik 1, 195–277.CrossRefGoogle Scholar
Härdle, W. & Mammen, E. (1993) Comparing nonparametric versus parametric regression fits. Annals of Statistics 21, 1926–1974.CrossRefGoogle Scholar
Hart, J.D. (1997) Nonparametric Smoothing and Lack-of-Fit Tests. Springer-Verlag.CrossRefGoogle Scholar
Heyde, C.C. (1997) Quasi-Likelihood and Its Applications. Springer-Verlag.CrossRefGoogle Scholar
Horowitz, J.L. & Härdle, W. (1994) Testing a parametric model against a semiparametric alternative. Econometric Theory 10, 821–848.CrossRefGoogle Scholar
Janssen, A. (1995) Principal component decomposition of non-parametric tests. Probability Theory and Related Fields 101, 193–209.CrossRefGoogle Scholar
Janssen, A. (2000) Global power functions of goodness of fit tests. Annals of Statistics 28, 239–253.CrossRefGoogle Scholar
Koul, H.L. & Stute, W. (1999) Nonparametric model checks for time series. Annals of Statistics 27, 204–236.CrossRefGoogle Scholar
Kress, R. (1999) Linear Integral Equations. Springer-Verlag.CrossRefGoogle Scholar
Milbrodt, H. & Strasser, H. (1990) On the asymptotic power of the two-sided Kolmogorov–Smirnov test. Journal of Statistical Planning and Inference 26, 1–23.CrossRefGoogle Scholar
Neuhaus, G. (1976) Asymptotic power properties of the Cramér–von Mises test under contiguous alternatives. Journal of Multivariate Analysis 6, 95–110.CrossRefGoogle Scholar
Newey, W.K. (1985) Maximum likelihood specification testing and conditional moment tests. Econometrica 53, 1047–1070.CrossRefGoogle Scholar
Nikitin, Y. (1995) Asymptotic Efficiency of Nonparametric Tests. Cambridge University Press.CrossRefGoogle Scholar
Rayner, J.C.W. & Best, D.J. (1989) Smooth Tests of Goodness of Fit. Oxford University Press.Google Scholar
Stinchcombe, M. & White, H. (1998) Consistent specification testing with nuisance parameters present only ùnder the alternative. Econometric Theory 14, 295–325.CrossRefGoogle Scholar
Stute, W. (1997) Nonparametric model checks for regression. Annals of Statistics 25, 613–641.CrossRefGoogle Scholar
Tauchen, G. (1985) Diagnostic testing and evaluation of maximum likelihood models. Journal of Econometrics 30, 415–443.CrossRefGoogle Scholar
Tjøstheim, D. (1986) Estimation in nonlinear time series models. Stochastic Processes and Their Applications 21, 251–273.CrossRefGoogle Scholar
Tripathi, G. & Kitamura, Y. (2003) Testing conditional moment restrictions. Annals of Statistics 31, 2059–2095.CrossRefGoogle Scholar
van der Vaart, A.W. & Wellner, J.A. (1996) Weak Convergence and Empirical Processes. Springer-Verlag.CrossRefGoogle Scholar
Whang, Y.-J. (2001) Consistent specification testing for conditional moment restrictions. Economics Letters 71, 299–306.CrossRefGoogle Scholar
Wooldridge, J. (1992) A test for functional form against nonparametric alternatives. Econometric Theory 8, 452–475.CrossRefGoogle Scholar
Yatchew, A.J. (1992) Nonparametric regression tests based on least squares. Econometric Theory 8, 435–451.CrossRefGoogle Scholar
Zheng, X. (1996) A consistent test of functional form via nonparametric estimation technique. Journal of Econometrics 75, 263–289.CrossRefGoogle Scholar