Tests for non-linear dynamics in systems of non-stationary economic time series: the case of short-term US interest rates

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.