IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Linear cointegration of nonlinear time series with an application to interest rate dynamics

  • Barry E. Jones
  • Travis D. Nesmith

We derive a definition of linear cointegration for nonlinear stochastic processes using a martingale representation theorem. The result shows that stationary linear cointegrations can exhibit nonlinear dynamics, in contrast with the normal assumption of linearity. We propose a sequential nonparametric method to test first for cointegration and second for nonlinear dynamics in the cointegrated system. We apply this method to weekly US interest rates constructed using a multirate filter rather than averaging. The Treasury Bill, Commercial Paper and Federal Funds rates are cointegrated, with two cointegrating vectors. Both cointegrations behave nonlinearly. Consequently, linear models will not fully replicate the dynamics of monetary policy transmission.

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://www.federalreserve.gov/pubs/feds/2007/200703/200703abs.html
Download Restriction: no

File URL: http://www.federalreserve.gov/pubs/feds/2007/200703/200703pap.pdf
Download Restriction: no

Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2007-03.

as
in new window

Length:
Date of creation: 2006
Date of revision:
Handle: RePEc:fip:fedgfe:2007-03
Contact details of provider: Postal:
20th Street and Constitution Avenue, NW, Washington, DC 20551

Web page: http://www.federalreserve.gov/

More information through EDIRC

Order Information: Web: http://www.federalreserve.gov/pubs/feds/fedsorder.html

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. Choi, Woon Gyu, 1999. "Asymmetric Monetary Effects on Interest Rates across Monetary Policy Stances," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(3), pages 386-416, August.
  2. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
  3. William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 1996. "A Single-Blind Controlled Competition among Tests for Nonlinearity and Chaos," Econometrics 9602005, EconWPA, revised 20 Sep 1996.
  4. Jerry Coakley & Ana-Maria Fuertes, 2001. "Nonparametric cointegration analysis of real exchange rates," Applied Financial Economics, Taylor & Francis Journals, vol. 11(1), pages 1-8.
  5. repec:cup:macdyn:v:5:y:2001:i:3:p:380-412 is not listed on IDEAS
  6. David K. Backus, 1993. "Long-Memory Inflation Uncertainty: Evidence from the Term Structure of Interest Rates," Working Papers 93-04, New York University, Leonard N. Stern School of Business, Department of Economics.
  7. Karanasos, M. & Sekioua, S.H. & Zeng, N., 2006. "On the order of integration of monthly US ex-ante and ex-post real interest rates: New evidence from over a century of data," Economics Letters, Elsevier, vol. 90(2), pages 163-169, February.
  8. Hinich, Melvin A. & Wild, Phillip, 2001. "Testing Time-Series Stationarity Against An Alternative Whose Mean Is Periodic," Macroeconomic Dynamics, Cambridge University Press, vol. 5(03), pages 380-412, June.
  9. Maki, Daiki, 2003. "Nonparametric cointegration analysis of the nominal interest rate and expected inflation rate," Economics Letters, Elsevier, vol. 81(3), pages 349-354, December.
  10. Young-Sook Lee & Tae-Hwan Kim & Paul Newbold, 2004. "Spurious Nonlinear Regressions In Econometrics," Royal Economic Society Annual Conference 2004 27, Royal Economic Society.
  11. Pantula, Sastry G., 1989. "Testing for Unit Roots in Time Series Data," Econometric Theory, Cambridge University Press, vol. 5(02), pages 256-271, August.
  12. Hinich, Melvin J & Patterson, Douglas M, 1985. "Evidence of Nonlinearity in Daily Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(1), pages 69-77, January.
  13. Psaradakis Zacharias & Sola Martin & Spagnolo Fabio, 2006. "Instrumental-Variables Estimation in Markov Switching Models with Endogenous Explanatory Variables: An Application to the Term Structure of Interest Rates," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(2), pages 1-31, May.
  14. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  15. G. Pfann & P. Schotman & R. Tschernig, 1994. "Nonlinear Interest Rate Dynamics and Implications for the Term Structure," SFB 373 Discussion Papers 1994,43, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  16. Calza, Alessandro & Sousa, João, 2005. "Output and inflation responses to credit shocks: are there threshold effects in the euro area?," Working Paper Series 0481, European Central Bank.
  17. Johansen, S., 1991. "Determination of Cointegration Rank in the Presence of a Linear Trend," Papers 76a, Helsinki - Department of Economics.
  18. Hinich Melvin J & Mendes Eduardo M & Stone Lewi, 2005. "Detecting Nonlinearity in Time Series: Surrogate and Bootstrap Approaches," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-15, December.
  19. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  20. Hinich , Melvin J. & Rothman, Philip, 1998. "Frequency-Domain Test Of Time Reversibility," Macroeconomic Dynamics, Cambridge University Press, vol. 2(01), pages 72-88, March.
  21. Bierens, H.J., 1995. "Nonparametric cointegration analysis," Discussion Paper 1995-123, Tilburg University, Center for Economic Research.
  22. repec:cup:macdyn:v:2:y:1998:i:1:p:72-88 is not listed on IDEAS
  23. Rapach, David E. & Weber, Christian E., 2004. "Are real interest rates really nonstationary? New evidence from tests with good size and power," Journal of Macroeconomics, Elsevier, vol. 26(3), pages 409-430, September.
  24. Gil-Alana, Luis A., 2004. "Long memory in the U.S. interest rate," International Review of Financial Analysis, Elsevier, vol. 13(3), pages 265-276.
  25. Tsay, Wen-Jen, 2000. "Long memory story of the real interest rate," Economics Letters, Elsevier, vol. 67(3), pages 325-330, June.
  26. Barnett, William A. & Ronald Gallant, A. & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1995. "Robustness of nonlinearity and chaos tests to measurement error, inference method, and sample size," Journal of Economic Behavior & Organization, Elsevier, vol. 27(2), pages 301-320, July.
Full references (including those not matched with items on IDEAS)

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

When requesting a correction, please mention this item's handle: RePEc:fip:fedgfe:2007-03. 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: (Marlene Vikor)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.