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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.

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File URL: http://www.federalreserve.gov/pubs/feds/2007/200703/200703pap.pdf
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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.

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Date of creation: 2006
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Handle: RePEc:fip:fedgfe:2007-03
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  11. Johansen, S., 1991. "Determination of Cointegration Rank in the Presence of a Linear Trend," Papers 76a, Helsinki - Department of Economics.
  12. 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.
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  26. 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.
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