A Test of the Martingale Hypothesis
AbstractThis paper proposes a statistical test of the martingale hypothesis. It can be used to test whether a given time series is a martingale process against certain non-martingale alternatives. The class of alternative processes against which our test has power is very general and it encompasses many nonlinear non-martingale processes which may not be detected using traditional spectrum-based or variance-ratio tests. We look at the hypothesis of martingale, in contrast with other existing methods which test for the hypothesis of martingale difference. Two different types of test are considered: one is a generalized Kolmogorov-Smirnov test and the other is a Cramer-von Mises type test. For the processes that are first-order Markovian in mean, in particular, our approach yields the test statistics that neither depend upon any smoothing parameter nor require any resampling procedure to simulate the null distributions. Their null limiting distributions are nicely characterized as functionals of a continuous stochastic process so that the critical values are easily tabulated. We prove consistency of our tests and further investigate their finite sample properties via simulation. Our tests are found to be rather powerful in moderate size samples against a wide variety of non-martingales including exponential autoregressive, threshold autoregressive, markov switching, chaotic, and some of nonstationary processes.
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Bibliographic InfoArticle provided by De Gruyter in its journal Studies in Nonlinear Dynamics & Econometrics.
Volume (Year): 9 (2005)
Issue (Month): 2 (June)
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Web page: http://www.degruyter.com
Other versions of this item:
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
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.:
- Park, Joon Y. & Phillips, Peter C.B., 1999.
"Asymptotics For Nonlinear Transformations Of Integrated Time Series,"
Cambridge University Press, vol. 15(03), pages 269-298, June.
- Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Bierens, H.J. & Ploberger, W., 1995.
"Asymptotic theory of integrated conditional moment tests,"
1995-124, Tilburg University, Center for Economic Research.
- Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
- de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
- Enders, Walter & Granger, C. W. J., 1998.
"Unit Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates,"
Staff General Research Papers
1388, Iowa State University, Department of Economics.
- Enders, Walter & Granger, Clive W J, 1998. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 304-11, July.
- Tom Doan, . "RATS programs to replicate Enders/Granger JBES(1998)on threshold unit roots," Statistical Software Components RTZ00054, Boston College Department of Economics.
- Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
- Andrews, Donald W. K., 1987.
"Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables,"
645, California Institute of Technology, Division of the Humanities and Social Sciences.
- Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
- Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, vol. 98(1), pages 27-46, September.
- Manuel A. Dominguez & Ignacio N. Lobato, 2001. "A Consistent Test for the Martingale Difference Hypothesis," Working Papers 0101, Centro de Investigacion Economica, ITAM.
- Bierens, H.J., 1989.
"A consistent conditional moment test of functional form,"
Serie Research Memoranda
0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
- Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
- Donald W.K. Andrews, 1996.
"A Conditional Kolmogorov Test,"
Cowles Foundation Discussion Papers
1111R, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Chung-Ming Kuan & Wei-Ming Lee, 2003.
"A New Test of the Martingale Difference Hypothesis,"
IEAS Working Paper : academic research
03-A001, Institute of Economics, Academia Sinica, Taipei, Taiwan.
- Kuan Chung-Ming & Lee Wei-Ming, 2004. "A New Test of the Martingale Difference Hypothesis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(4), pages 1-26, December.
- Joon Y. Park & Yoosoon Chang, 2004. "Endogeneity in Nonlinear Regressions with Integrated Time Series," Econometric Society 2004 North American Winter Meetings 594, Econometric Society.
- Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
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