Modelling Nonstationary Time Series using Trend-Stationary Hypothesis

Abstract: This paper challenges the prevalence of unit root models by introducing the Linear Trend-Stationary Trigonometric ARMA (LTSTA), a novel framework for modelling nonstationary time series under the trend-stationary hypothesis. LTSTA decomposes series into three components: (1) a deterministic trend (modelled via continuous piecewise linear functions with structural breaks), (2) a Fourier-based deterministic seasonality component, and (3) a stochastic ARMA error term. We propose a heuristic approach to determine the optimal number of structural breaks, with parameter estimation performed through an iterative scheme that integrates a modified dynamic programming algorithm for break detection and a standard regression procedure with ARMA errors. The model's performance is evaluated through a case study on US Real GDP (2002-2025), where it accurately identifies breaks corresponding to major economic events (e.g., the 2008 financial crisis and COVID-19 shocks). Additionally, LTSTA outperforms well-established univariate statistical models (SES, Theta, TBATS, ETS, ARIMA, and Prophet) on the CIF 2016 forecasting competition dataset across MAE, RMSE, sMAPE, and MASE metrics. The LTSTA model provides an interpretable alternative to unit root approaches, particularly suited for time series with predominant deterministic properties where structural break detection is critical.