A Test of the Martingale Hypothesis
This 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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 9 (2005)
Issue (Month): 2 (June)
|Contact details of provider:|| Web page: https://www.degruyter.com|
|Order Information:||Web: https://www.degruyter.com/view/j/snde|
References listed on IDEAS
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.:
- Manuel A. Dominguez & Ignacio N. Lobato, 2001. "A Consistent Test for the Martingale Difference Hypothesis," Working Papers 0101, Centro de Investigacion Economica, ITAM.
- Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, 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.
- Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
- 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.
- Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-987, December.
- 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 1443-1458, November.
- 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 Archive
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 304-311, July.
- Tom Doan, "undated". "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.
- Joon Y. Park & Yoosoon Chang, 2004. "Endogeneity in Nonlinear Regressions with Integrated Time Series," Econometric Society 2004 North American Winter Meetings 594, Econometric Society.
- 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.
- 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.
- 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.
- de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
- Andrews, Donald W.K., 1988.
"Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables,"
Cambridge University Press, vol. 4(03), pages 458-467, December.
- Andrews, Donald W. K., 1987. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Working Papers 645, California Institute of Technology, Division of the Humanities and Social Sciences.
- Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, vol. 98(1), pages 27-46, September.
When requesting a correction, please mention this item's handle: RePEc:bpj:sndecm:v:9:y:2005:i:2:n:2. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Peter Golla)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.