Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and interest rate

This paper is concerned with testing the unit root with drift hypothesis against a very general trend stationarity hypothesis, namely the alternative that the time series is stationary about an almost arbitrary deterministic function of time. Our approach employs the fact that any function of time can be approximated arbitrarily close by a linear function of Chebishev polynomials. We propose various tests on the basis of an Augmented Dickey-Fuller auxiliary regression with linear and nonlinear deterministic trends, where the nonlinear deterministic trend is approximated by detrended Chebishev time polynomials. Also, we propose a model-free test. We apply our tests to the GNP deflator, the consumer price index, and the interest rate for the USA, taken from the extended Nelson-Plosser data set. The results indicate that these series are nonlinear trend stationary.