Advanced Search
MyIDEAS: Login to save this paper or follow this series

Regression asymptotics using martingale convergence methods

Contents:

Author Info

  • Ibragimov, Rustam
  • Phillips, Peter C.B.

Abstract

Weak convergence of partial sums and multilinear forms in independent random variables and linear processes and their nonlinear analogues to stochastic integrals now plays a major role in nonstationary time series and has been central to the development of unit root econometrics. The present paper develops a new and conceptually simple method for obtaining such forms of convergence. The method relies on the fact that the econometric quantities of interest involve discrete time martingales or semimartingales and shows how in the limit these quantities become continuous martingales and semimartingales. The limit theory itself uses very general convergence results for semimartingales that were obtained in the work of Jacod and Shiryaev (2003, Limit Theorems for Stochastic Processes). The theory that is developed here is applicable in a wide range of econometric models, and many examples are given. %One notable outcome of the new approach is that it provides a unified treatment of the asymptotics for stationary, explosive, unit root, and local to unity autoregression, and also some general nonlinear time series regressions. All of these cases are subsumed within the martingale convergence approach, and different rates of convergence are accommodated in a natural way. Moreover, the results on multivariate extensions developed in the paper deliver a unification of the asymptotics for, among many others, models with cointegration and also for regressions with regressors that are nonlinear transforms of integrated time series driven by shocks correlated with the equation errors. Because this is the first time the methods have been used in econometrics, the exposition is presented in some detail with illustrations of new derivations of some well-known existing results, in addition to the provision of new results and the unification of the limit theory for autoregression.

Download Info

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.
File URL: http://dash.harvard.edu/bitstream/handle/1/2624459/ibragimov_martingale.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Harvard University Department of Economics in its series Scholarly Articles with number 2624459.

as in new window
Length:
Date of creation: 2008
Date of revision:
Publication status: Published in Econometric Theory
Handle: RePEc:hrv:faseco:2624459

Contact details of provider:
Postal: Littauer Center, Cambridge, MA 02138
Phone: 617-495-2144
Fax: 617-495-7730
Web page: http://www.economics.harvard.edu/
More information through EDIRC

Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:

References

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.:
as in new window
  1. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(04), pages 888-947, August.
  2. L Giraitis & P C B Phillips, . "Uniform limit theory for stationary autoregression," Discussion Papers 05/23, Department of Economics, University of York.
  3. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  4. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
  5. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  6. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  7. 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.
  8. Peter C.B. Phillips, 1999. "Unit Root Log Periodogram Regression," Cowles Foundation Discussion Papers 1244, Cowles Foundation for Research in Economics, Yale University.
  9. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonlinear Regressions with Integrated Time Series," Working Paper Series no6, Institute of Economic Research, Seoul National University.
  10. Saikkonen, Pentti & Choi, In, 2004. "Cointegrating Smooth Transition Regressions," Econometric Theory, Cambridge University Press, vol. 20(02), pages 301-340, April.
  11. Nze, Patrick Ango & Doukhan, Paul, 2004. "Weak Dependence: Models And Applications To Econometrics," Econometric Theory, Cambridge University Press, vol. 20(06), pages 995-1045, December.
  12. P tscher, Benedikt M., 2004. "Nonlinear Functions And Convergence To Brownian Motion: Beyond The Continuous Mapping Theorem," Econometric Theory, Cambridge University Press, vol. 20(01), pages 1-22, February.
  13. Peter C.B. Phillips & Tassos Magdalinos, 2004. "Limit Theory for Moderate Deviations from a Unit Root," Cowles Foundation Discussion Papers 1471, Cowles Foundation for Research in Economics, Yale University.
  14. In Choi & Pentti Saikkonen, 2004. "Testing linearity in cointegrating smooth transition regressions," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 341-365, December.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. M.C. Medeiros & E. Mendes & Les Oxley, 2010. "A Note on Nonlinear Cointegration, Misspecification and Bimodality," Working Papers in Economics 10/01, University of Canterbury, Department of Economics and Finance.
  2. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(04), pages 888-947, August.
  3. Ioannis Kasparis & Peter C.B. Phillips & Tassos Magdalinos, 2012. "Non-linearity Induced Weak Instrumentation," University of Cyprus Working Papers in Economics 02-2012, University of Cyprus Department of Economics.
  4. Yoosoon Chang, 2004. "Taking a New Contour: A Novel Approach to Panel Unit Root Tests," Econometric Society 2004 Far Eastern Meetings 796, Econometric Society.
  5. Hong, Seung Hyun & Phillips, Peter C. B., 2010. "Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 96-114.
  6. Bent Nielsen & Carlos Caceres, 2007. "Convergence to Stochastic Integrals with Non-linear Integrands," Economics Series Working Papers 2007-W02, University of Oxford, Department of Economics.
  7. Pötscher, Benedikt M., 2013. "On The Order Of Magnitude Of Sums Of Negative Powers Of Integrated Processes," Econometric Theory, Cambridge University Press, vol. 29(03), pages 642-658, June.
  8. Peter C.B. Phillips & Degui Li & Jiti Gao, 2013. "Estimating Smooth Structural Change in Cointegration Models," Cowles Foundation Discussion Papers 1910, Cowles Foundation for Research in Economics, Yale University.
  9. Wagner, Martin, 2012. "The Phillips unit root tests for polynomials of integrated processes," Economics Letters, Elsevier, vol. 114(3), pages 299-303.
  10. MArcelo Cunha Medeiros & Eduardo Mendes & Les Oxley, 2010. "Nonlinear Cointegration, Misspecification and Bimodality," Textos para discussão 577, Department of Economics PUC-Rio (Brazil).

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:hrv:faseco:2624459. 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: (Ben Steinberg).

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.