Nonparametric Nonlinear Cotrending 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, hence the series have common nonlinear deterministic time trends.In this paper we shall develop nonparametric tests for nonlinear co-trending.The 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 nonlinearly co-trended, where the nonlinear trend in the inflation rate is positively related to the nonlinear trend in the interest rate.This positive relation between interest and inflation is known in the literature as the price puzzle. Thus, our result suggests that the price puzzle is due to a common nonlinear time trend in the series involved.