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Linear cointegration of nonlinear time series with an application to interest rate dynamics

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Abstract

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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  • Barry E. Jones & Travis D. Nesmith, 2006. "Linear cointegration of nonlinear time series with an application to interest rate dynamics," Finance and Economics Discussion Series 2007-03, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2007-03
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    1. Lahiani, Amine & Hammoudeh, Shawkat & Gupta, Rangan, 2016. "Linkages between financial sector CDS spreads and macroeconomic influence in a nonlinear setting," International Review of Economics & Finance, Elsevier, vol. 43(C), pages 443-456.
    2. Trofimov, Ivan D., 2013. "Nonparametric Approach to Portfolio Diversification: The Case of Australian Equity Market - Un approccio non-parametrico alla diversificazione del portafoglio: il caso del mercato azionario australian," Economia Internazionale / International Economics, Camera di Commercio Industria Artigianato Agricoltura di Genova, vol. 66(1), pages 87-112.
    3. Trofimov, Ivan D., 2013. "Nonparametric approach to portfolio diversification: the case of Australian equity market," MPRA Paper 79562, University Library of Munich, Germany.

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    time series analysis; Cointegration; Interest rates;
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