Identifying trend nature in time series using autocorrelation functions and stationarity tests

Time series non-stationarity can be detected thanks to autocorrelation functions. But trend nature, either deterministic or either stochastic, is not identifiable. Strategies based on Dickey-Fuller unit root-test are appropriate to choose between a linear deterministic trend or a stochastic trend. But all the observed deterministic trends are not linear, and such strategies fail in detecting a quadratic deterministic trend. Being a confounding factor, a quadratic deterministic trend makes a unit root spuriously appear. We provide a new procedure, based on Ouliaris-Park-Phillips unit root test, convenient for time series containing polynomial trends with a degree higher than one. Our approach is assessed based on simulated data. The strategy is finally applied on two real datasets: money stock in USA and on CO2 atmospheric concentration. Compared with Dickey-Fuller diagnosis, our strategy provides the model with the best performances.