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AN IMPROVED GENERALIZED SPECTRAL TEST FOR CONDITIONAL MEAN MODELS IN TIME SERIES WITH CONDITIONAL HETEROSKEDASTICITY OF UNKNOWN FORM

Published online by Cambridge University Press:  06 December 2006

Yongmiao Hong  and
Yoon-Jin Lee
Yongmiao Hong
Affiliation:
Cornell University and Xiamen University
Yoon-Jin Lee
Affiliation:
Indiana University
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Abstract

Dynamic economic theories usually have implications on and only on the conditional mean dynamics of economic processes. Using a generalized spectral derivative approach, Hong and Lee (2005, Review of Economic Studies 72, 499–541) recently proposed a new class of omnibus nonparametric specification tests for linear and nonlinear time series conditional mean models, where the dimension of the conditioning information set may be infinite. The tests can detect a wide range of model misspecifications in mean while being robust to conditional heteroskedasticity and time-varying higher order moments of unknown form. They enjoy an asymptotic “nuisance parameter–free” property in the sense that parameter estimation uncertainty has no impact on the asymptotic N(0,1) distribution of the test statistics. As a result, only the estimated residuals from the null parametric model are needed to implement the tests, and no specific estimation is required.

Although parameter estimation uncertainty has no impact on the asymptotic distribution of the tests, it may have significant impact on the finite-sample distribution, and such an impact may become more substantial as the number of estimated parameters increases. In this paper, we adopt the Wooldridge (1990, Econometric Theory 6, 17–43) device for parametric m-tests to the Hong and Lee (2005) nonparametric tests to reduce the impact of parameter estimation uncertainty. Asymptotic size and power properties of the modified tests are investigated, and simulation studies show that the modified tests generally have better sizes in finite samples and are robust to parameter estimation uncertainty. In the meantime, the size improvement does not cause loss of power against a wide range of alternatives when using the empirical critical values for the tests. These results suggest that the modified generalized spectral derivative tests can be a useful tool in time series conditional mean modeling.We thank Bruce Hansen (the co-editor) and three referees for insightful and helpful comments and suggestions. We also are grateful for financial support from the National Science Foundation Grant SES–0111769 and the Cheung Kong Visiting Scholarship by the Chinese Ministry of Education and Xiamen University, China.

Type
Research Article
Information
Econometric Theory , Volume 23 , Issue 1 , February 2007 , pp. 106 - 154
Copyright
© 2007 Cambridge University Press

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References

REFERENCES

Adda, J. & R. Cooper (2003) Dynamic Economics: Quantitative Methods and Applications. MIT Press.
Bierens, H. (1982) Consistent model specification tests. Journal of Econometrics 20, 105–134.Google Scholar
Brillinger, D. (1965) An introduction to polyspectra. Annals of Mathematical Statistics 36, 1351–1374.Google Scholar
Brillinger, D. & M. Rosenblatt (1967a) Asymptotic theory of estimates of k-th order spectra. In B. Harris (ed.), Spectral Analysis of Time Series, pp. 153–188. Wiley.
Brillinger, D. & M. Rosenblatt (1967b) Computation and interpretation of k-th order spectra. In B. Harris (ed.), Spectral Analysis of Time Series, pp. 189–232. Wiley.
Chen, W. & R. Deo (2004) Power transformations to induce normality and their applications. Journal of the Royal Statistical Society, Series B 66, 117–130.Google Scholar
Cochrane, J. (2001) Asset Pricing. Princeton University Press.
Diebold, F.X. & G.D. Rudebusch (1990) A nonparametric investigation of duration dependence in the American business cycle. Journal of Political Economy 98, 596–616.Google Scholar
Engle, R.F., D. Lilien, & R.P. Robins (1987) Estimating time-varying risk premia in the term structure: The ARCH-M model. Econometrica 55, 391–407.Google Scholar
Engle, R.F. & J. Russell (1998) Autoregressive conditional duration: A new model for irregularly spaced transaction data. Econometrica 66, 1127–1162.Google Scholar
Gallant, A.R., D. Hsieh, & G. Tauchen (1991) On fitting a recalcitrant series: The pound/dollar exchange rate, 1974–83. In W. Barnett, J. Powell, & G. Tauchen (eds.), Nonparametric and Semiparametric Methods in Econometrics and Statistics, Proceedings of the Fifth International Symposium in Economic Theory and Econometrics, pp. 199–240. Cambridge University Press.
Gonçalves, S. & L. Kilian (2004) Bootstrapping autoregressions with conditional heteroskedasticity of unknown form. Journal of Econometrics 123, 89–120.Google Scholar
Granger, C.W.J. & T. Teräsvirta (1993) Modelling Nonlinear Economic Relationships. Oxford University Press.
Hamilton, J.D. (1989) A new approach to economic analysis of nonstationary time series and the business cycle. Econometrica 57, 357–384.Google Scholar
Hamilton, J.D. & G. Lin (1996) Stock market volatility and the business cycles. Journal of Applied Econometrics 11, 573–593.Google Scholar
Hansen, B. (1994) Autoregressive conditional density estimation. International Economic Review 35, 705–730.Google Scholar
Hansen, B. (1996) Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 64, 413–430.Google Scholar
Hansen, B. (2000) Sample splitting and threshold estimation. Econometrica 68, 575–603.Google Scholar
Harvey, C. & A. Siddique (1999) Autoregressive conditional skewness. Journal of Financial and Quantitative Analysis 34, 465–487.Google Scholar
Harvey, C. & A. Siddique (2000) Conditional skewness in asset pricing tests. Journal of Finance 55, 1263–1296.Google Scholar
Hausman, J. (1978) Specification tests in econometrics. Econometrica 46, 1251–1271.Google Scholar
Hong, Y. (1999) Hypothesis testing in time series via the empirical characteristic function: A generalized spectral density approach. Journal of the American Statistical Association 84, 1201–1220.Google Scholar
Hong, Y. & T.-H. Lee (2003) Diagnostic checking for adequacy of nonlinear time series models. Econometric Theory 19, 1065–1121.Google Scholar
Hong, Y. & Y.-J. Lee (2005) Generalized spectral tests for conditional mean models in time series with conditional heteroskedasticity of unknown form. Review of Economic Studies 72, 499–541.Google Scholar
Horowitz, J. (2003) Bootstrap methods for Markov processes. Econometrica 71, 1049–1082.Google Scholar
Jondeau, E. & M. Rockinger (2003) Conditional volatility, skewness, and kurtosis: Existence, persistence, and comovements. Journal of Economic Dynamics and Control 27, 1699–1737.Google Scholar
Kim, W. & O. Linton (2004) The live methods for generalized additive volatility models. Econometric Theory 20, 1094–1139.Google Scholar
Potter, S. (1995) A nonlinear approach to U.S. GNP. Journal of Applied Econometrics 10, 109–125.Google Scholar
Priestley, M. (1981) Spectral Analysis and Time Series. Academic Press.
Priestley, M. (1988) Non-Linear and Non-Stationary Time Series Analysis. Academic Press.
Sargent, T. & L. Ljungqvist (2002) Recursive Macroeconomic Theory. MIT Press.
Schwert, G.W. (1989) Why does stock market volatility change over time? Journal of Finance 44, 1115–1153.Google Scholar
Stinchcombe, M. & H. White (1998) Consistent specification testing with nuisance parameters present only under the alternative. Econometric Theory 14, 295–324.Google Scholar
Subba Rao, T. & M. Gabr (1984) Introduction to Bispectral Analysis and Bilinear Time Series Models, Lecture Notes in Statistics 24. Springer-Verlag.
Teräsvirta, T. (1994) Specification, estimation and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association 89, 208–218.Google Scholar
Tong, H. (1990) Nonlinear Time Series: A Dynamic System Approach. Clarendon Press.
White, H. (1987) Specification testing in dynamic models. In T. Bewley (ed.), Advances in Econometrics—Fifth World Congress, vol. 1, pp. 1–58. Cambridge University Press.
White, H. (1994) Estimation, Inference and Specification Analysis. Cambridge University Press.
White, H. (2001) Asymptotic Theory for Econometricians, 2nd ed. Academic Press.
Wooldridge, J. (1990a) A unified approach to robust, regression-based specification tests. Econometric Theory 6, 17–43.Google Scholar
Wooldridge, J. (1990b) An encompassing approach to conditional mean tests with applications to testing nonnested hypotheses. Journal of Eonometrics 45, 331–350.Google Scholar
Wooldridge, J. (1991) On the application of robust, regression-based diagnostics to models of conditional means and conditional variances. Journal of Econometrics 47, 5–46.Google Scholar