Nonparametric Nonlinear Co-Trending Analysis, With an Application to Interest and Inflation in the U.S

Given the assumption that the components of a vector time series are stationary about nonlinear deterministic time trends, nonlinear co-trending is the phenomenon that one or more linear combinations of the time series are stationary about a linear trend or a constant, hence the series have common nonlinear deterministic time trends. In this paper we develop nonparametric tests for nonlinear cotrending. These tests are based on generalized eigenvalues, where the two matrices involved are constructed nonparametrically on the basis of partial sums. We apply this approach to the federal funds rate and the CPI inflation rate in the U.S., using monthly data. It appears that these series are nonlinear co-trended, where the nonlinear trend in the inflation rate is positively related to the nonlinear trend in the interest rate. Moreover, the price puzzle seems to a large extent due to this common nonlinear trend. Furthermore, the common nonlinear trend seems to be related to the oil price shocks induced by the OPEC cartel in the early and late seventies.