Testing the Martingale Difference Hypothesis Using Integrated Regression Functions
This paper proposes an omnibus test for testing a generalized version of the martingale difference hypothesis (MDH). This generalized hypothesis includes the usual MDH, testing for conditional moments constancy such as conditional homoscedasticity (ARCH effects) or testing for directional predictability. Here we propose a unified approach for dealing with all of these testing problems. These hypotheses are long standing problems in econometric time series analysis, and typically have been tested using the sample autocorrelations or in the spectral domain using the periodogram. Since these hypotheses cover also nonlinear predictability, tests based on those second order statistics are inconsistent against uncorrelated processes in the alternative hypothesis. To circumvent this problem we introduce the pairwise integrated regression functions as measures of linear and nonlinear dependence. With our test there is no need to choose a lag order depending on sample size, to smooth the data or to formulate a parametric alternative model. Moreover, our test is robust to higher order dependence, in particular to conditional heteroskedasticity. Under general dependence the asymptotic null distribution depends on the data generating process, so a bootstrap procedure is considered and a Monte Carlo study examines its finite sample performance. Then we investigate the martingale and conditional heteroskedasticity properties of the Pound/Dollar exchange rate.
|Date of creation:||01 May 2006|
|Date of revision:|
|Publication status:||Forthcoming, Computational Statistics and Data Analysis|
|Contact details of provider:|| Web page: http://www.unav.edu/web/facultad-de-ciencias-economicas-y-empresariales|
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- de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
- John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
- Durlauf, Steven N., 1991.
"Spectral based testing of the martingale hypothesis,"
Journal of Econometrics,
Elsevier, vol. 50(3), pages 355-376, December.
- Steven N. Durlauf, 1992. "Spectral Based Testing of the Martingale Hypothesis," NBER Technical Working Papers 0090, National Bureau of Economic Research, Inc.
- Herman J. Bierens & Werner Ploberger, 1997.
"Asymptotic Theory of Integrated Conditional Moment Tests,"
Econometric Society, vol. 65(5), pages 1129-1152, September.
- Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 1995-124, Tilburg University, Center for Economic Research.
- Emmanuel Guerre & Pascal Lavergne, 2001. "Rate-optimal data-driven specification testing in regression models," Econometrics 0107001, EconWPA.
- Manuel A. Domínguez & Ignacio N. Lobato, 2004. "Consistent Estimation of Models Defined by Conditional Moment Restrictions," Econometrica, Econometric Society, vol. 72(5), pages 1601-1615, 09.
- Escanciano, J. Carlos & Velasco, Carlos, 2006.
"Generalized spectral tests for the martingale difference hypothesis,"
Journal of Econometrics,
Elsevier, vol. 134(1), pages 151-185, September.
- Velasco, Carlos & Escanciano, Juan Carlos, 2003. "Generalized spectral tests for the martingale difference hypothesis," DES - Working Papers. Statistics and Econometrics. WS ws035312, Universidad Carlos III de Madrid. Departamento de Estadística.
- Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December.
- Chen, Xiaohong & White, Halbert, 1996. "Laws of Large Numbers for Hilbert Space-Valued Mixingales with Applications," Econometric Theory, Cambridge University Press, vol. 12(02), pages 284-304, June.
- Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
- Yongmiao Hong & Tae-Hwy Lee, 2003. "Inference on Predictability of Foreign Exchange Rates via Generalized Spectrum and Nonlinear Time Series Models," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1048-1062, November.
- Bera, Anil K & Higgins, Matthew L, 1997. "ARCH and Bilinearity as Competing Models for Nonlinear Dependence," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 43-50, January.
- Enno Mammen, .
"Comparing nonparametric versus parametric regression fits,"
Statistic und Oekonometrie
9205, Humboldt Universitaet Berlin.
- Hardle, W. & Mammen, E., 1990. "Comparing nonparametric versus parametric regression fits," CORE Discussion Papers 1990065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, vol. 98(1), pages 27-46, September.
- Linton, O. & Whang, Yoon-Jae, 2007. "The quantilogram: With an application to evaluating directional predictability," Journal of Econometrics, Elsevier, vol. 141(1), pages 250-282, November.
- Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
- Juan Carlos Escanciano, 2004. "Model Checks Using Residual Marked Empirical Processes," Faculty Working Papers 13/04, School of Economics and Business Administration, University of Navarra.
- Chen, Xiaohong & Fan, Yanqin, 1999. "Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series," Journal of Econometrics, Elsevier, vol. 91(2), pages 373-401, August.
- Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
- Chen, Xiaohong & White, Halbert, 1998. "Central Limit And Functional Central Limit Theorems For Hilbert-Valued Dependent Heterogeneous Arrays With Applications," Econometric Theory, Cambridge University Press, vol. 14(02), pages 260-284, April.
- Hsieh, David A, 1989. "Testing for Nonlinear Dependence in Daily Foreign Exchange Rates," The Journal of Business, University of Chicago Press, vol. 62(3), pages 339-68, July.
- Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
- Ferreira, E. & Stute, W., 2004. "Testing for Differences Between Conditional Means in a Time Series Context," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 169-174, January.
- Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-64, July.
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