Abstract: Using Hall and Heyde's (1980) representation theorem, we show that the stationary co-integration relations of an integrated system are generally non-linear stochastic processes. We propose a sequential non-parametric procedure to test stationary co-integration relations for non-linear dynamics, and apply this procedure to short term U.S. interest rates as an illustration. We demonstrate that the weekly federal funds rate is co-integrated with Treasury bill and commercial paper rates and that the co-integration relations are non-linear.

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