Linear cointegration of nonlinear time series with an application to interest rate dynamics
AbstractWe 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.
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Bibliographic InfoPaper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2007-03.
Date of creation: 2006
Date of revision:
Other versions of this item:
- Nesmith Travis D & Jones Barry E, 2008. "Linear Cointegration of Nonlinear Time Series with an Application to Interest Rate Dynamics," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(1), pages 1-18, March.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- C82 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data
- E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-03-31 (All new papers)
- NEP-ECM-2007-03-31 (Econometrics)
- NEP-FMK-2007-03-31 (Financial Markets)
- NEP-MAC-2007-03-31 (Macroeconomics)
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- Bierens, Herman J., 1997.
"Nonparametric cointegration analysis,"
Journal of Econometrics,
Elsevier, vol. 77(2), pages 379-404, April.
- 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.
- 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.
- Pantula, Sastry G., 1989. "Testing for Unit Roots in Time Series Data," Econometric Theory, Cambridge University Press, vol. 5(02), pages 256-271, August.
- 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.
- 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.
- 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.
- 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.
- 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.
- repec:cup:macdyn:v:5:y:2001:i:3:p:380-412 is not listed on IDEAS
- 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.
- 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.
- 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.
- 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.
- Pfann, G.A. & Tschernig, R. & Schotman, Peter C., 1996. "Nonlinear interest rate dynamics and implications for the term structure," Open Access publications from Maastricht University urn:nbn:nl:ui:27-5920, Maastricht University.
- 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.
- Young-Sook Lee & Tae-Hwan Kim & Paul Newbold, 2004.
"Spurious Nonlinear Regressions In Econometrics,"
Royal Economic Society Annual Conference 2004
27, Royal Economic Society.
- 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 J. & Rothman, Philip, 1998.
"Frequency-Domain Test Of Time Reversibility,"
Cambridge University Press, vol. 2(01), pages 72-88, March.
- repec:cup:macdyn:v:2:y:1998:i:1:p:72-88 is not listed on IDEAS
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Tsay, Wen-Jen, 2000. "Long memory story of the real interest rate," Economics Letters, Elsevier, vol. 67(3), pages 325-330, June.
- 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.
- Jerry Coakley & Ana-Maria Fuertes, 2001. "Nonparametric cointegration analysis of real exchange rates," Applied Financial Economics, Taylor and Francis Journals, vol. 11(1), pages 1-8.
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