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

Authors: M. Boutahar; M. Royer-Carenzi

Addresses: CNRS, Centrale Marseille, Aix Marseille University, I2M, UMR 7373, Marseille, France ' CNRS, Centrale Marseille, Aix Marseille University, I2M, UMR 7373, Marseille, France

Abstract: 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.

Keywords: time series; stationarity; autocorrelation functions; unit root tests; Dickey-Fuller; KPSS; OPP test; trend detection; deterministic or stochastic trend; spurious unit root.

DOI: 10.1504/IJCEE.2024.135644

International Journal of Computational Economics and Econometrics, 2024 Vol.14 No.1, pp.1 - 22

Accepted: 25 Mar 2023
Published online: 20 Dec 2023 *

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