Linear cointegration of nonlinear time series with an application to interest rate dynamics
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.
|Date of creation:||2006|
|Date of revision:|
|Contact details of provider:|| Postal: |
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.:
- 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.
- 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,"
9602005, EconWPA, revised 20 Sep 1996.
- Barnett, William A. & Gallant, A. Ronald & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1997. "A single-blind controlled competition among tests for nonlinearity and chaos," Journal of Econometrics, Elsevier, vol. 82(1), pages 157-192.
- William Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 2012. "A Single-Blind Controlled Competition Among Tests For Nonlinearity And Chaos," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201219, University of Kansas, Department of Economics, revised Sep 2012.
- Bierens, H.J., 1995.
"Nonparametric cointegration analysis,"
1995-123, Tilburg University, Center for Economic Research.
- 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.
- Backus, David K & Zin, Stanley E, 1993.
"Long-Memory Inflation Uncertainty: Evidence from the Term Structure of Interest Rates,"
Journal of Money, Credit and Banking,
Blackwell Publishing, vol. 25(3), pages 681-700, August.
- David K. Backus & Stanley E. Zin, 1993. "Long-memory inflation uncertainty: evidence from the term structure of interest rates," Proceedings, Federal Reserve Bank of Cleveland, pages 681-708.
- 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.
- David K. Backus & Stanley E. Zin, 1993. "Long-memory Inflation Uncertainty: Evidence from the Term Structure of Interest Rates," NBER Technical Working Papers 0133, National Bureau of Economic Research, Inc.
- Menelaos Karananos & S.H Sekioua & N Zeng, 2005.
"On the order of integration of monthly US ex-ante and ex-post real interest rates new evidence from over a century of data,"
Money Macro and Finance (MMF) Research Group Conference 2005
21, Money Macro and Finance Research Group.
- 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.
- Hinich , Melvin J. & Rothman, Philip, 1998.
"Frequency-Domain Test Of Time Reversibility,"
Cambridge University Press, vol. 2(01), pages 72-88, March.
- 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.
- Calza Alessandro & Sousa João, 2006.
"Output and Inflation Responses to Credit Shocks: Are There Threshold Effects in the Euro Area?,"
Studies in Nonlinear Dynamics & Econometrics,
De Gruyter, vol. 10(2), pages 1-21, May.
- 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.
- 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.
- 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.
- Johansen, S., 1991.
"Determination of Cointegration Rank in the Presence of a Linear Trend,"
76a, Helsinki - Department of Economics.
- Johansen, Soren, 1992. "Determination of Cointegration Rank in the Presence of a Linear Trend," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 383-97, August.
- Tsay, Wen-Jen, 2000. "Long memory story of the real interest rate," Economics Letters, Elsevier, vol. 67(3), pages 325-330, June.
- Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
- 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.
- Lee, Young-Sook & Kim, Tae-Hwan & Newbold, Paul, 2005.
"Spurious nonlinear regressions in econometrics,"
Elsevier, vol. 87(3), pages 301-306, June.
- 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.
- Pfann, Gerard A. & Schotman, Peter C. & Tschernig, Rolf, 1996. "Nonlinear interest rate dynamics and implications for the term structure," Journal of Econometrics, Elsevier, vol. 74(1), pages 149-176, September.
- 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.
- repec:cup:macdyn:v:2:y:1998:i:1:p:72-88 is not listed on IDEAS
- Pantula, Sastry G., 1989. "Testing for Unit Roots in Time Series Data," Econometric Theory, Cambridge University Press, vol. 5(02), pages 256-271, August.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- repec:cup:macdyn:v:5:y:2001:i:3:p:380-412 is not listed on IDEAS
- 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.
- 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.
- 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.
- 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.
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: (Kris Vajs)
If references are entirely missing, you can add them using this form.