Rethinking Nonstationarity in Time Series: A Deterministic Trend Perspective

This paper challenges the dominance of stochastic trend models by introducing the Seasonal-Trend-Stationary ARMA (STSA) framework, which models univariate nonstationary time series as stationary fluctuations around deterministic trend and seasonal components, incorporating a finite number of structural breaks. We propose methods for estimating the locations and numbers of breaks using a modified dynamic programming algorithm and a sequential prediction-interval procedure, and we outline strategies for specifying and estimating the full model. Empirical analysis of U.S. Retail Sales (2004-2025) shows that the STSA model accurately identifies structural breaks corresponding to major economic events, including the Global Financial Crisis and the COVID-19 downturn. The decomposition into trend, seasonal, and ARMA components provides a realistic and interpretable representation of the underlying dynamics of the economic cycle, offering insights into the pace of growth within each regime, recurring seasonal patterns, and the persistence of short-term fluctuations. Although designed primarily for interpretability, STSA substantially outperforms Prophet and achieves forecasting accuracy comparable to state-of-the-art stochastic trend models (ARIMA, ETS, TBATS, Theta) on the M4 Competition monthly dataset, with particular advantages for series exhibiting abrupt structural changes, where stochastic models typically struggle to adapt.