Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Linear Cointegration of Nonlinear Time Series with an Application to Interest Rate Dynamics Barry E. Jones and Travis D. Nesmith 2007-03 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Linear Cointegration of Nonlinear Time Series with an Application to Interest Rate Dynamics Barry E. Jones Binghamton University Travis D. Nesmith Board of Governors of the Federal Reserve System November 29, 2006 Abstract We derive a denition 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 assump- tion of linearity. We propose a sequential nonparametric method to test rst for cointegration and second for nonlinear dynamics in the cointegrated system. We apply this method to weekly US interest rates constructed using a multirate lter 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. JEL Classication: C14; C32; C51; C82; E4 Keywords: cointegration; nonlinearity; interest rates; nonparametric estimation Corresponding author: 20th and C Sts., NW, Mail Stop 188, Washington, DC 20551 E-mail:
[email protected] Melvin Hinich provided technical advice on his bispectrum computer program.