February 2007

Linear Cointegration of Nonlinear Time Series with an Application to Interest Rate Dynamics

Barry E. Jones and 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 U.S. interest rates constructed using a multirate filter rather than averaging. The Treasury Bill, Commerical 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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Keywords: Cointegration; nonlinearity; interest rates; nonparametric estimation

PDF: Full Paper

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Last Update: October 19, 2020