Identifying trend nature in time series using autocorrelation functions and R-routines based on stationarity tests
Résumé
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 appear a unit root spuriously. We provide a new procedure, based on Ouliaris-Park-Phillips unit root test, convenient for time series containing polynomial trends with degree higher than one. Our approach is assessed on simulated data. The strategy is finally applied on two real datasets : number of terminated pregnancies in Québec, Canada, and atmospheric CO2 concentration. Compared with Dickey-Fuller diagnosis, our strategy provides the model with the best performances.
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