Rethinking Nonstationarity in Time Series: A Deterministic Trend Perspective

Abstract

This paper challenges the dominance of stochastic trend models by introducing the Seasonal-Trend-Stationary ARMA (STSA) framework, which represents univariate nonstationary time series as stationary fluctuations around deterministic trend and seasonal components, allowing for a finite number of structural breaks in the trend. We present methods for estimating the locations and number of breaks using a dynamic programming algorithm and a sequential prediction-interval-based procedure, respectively, and outline strategies for specifying and estimating the full model. Empirical analysis of U.S. exports of goods to Mainland China (2006-2025) demonstrates that the STSA model accurately identifies structural breaks linked to major economic events and provides a meaningful decomposition of the underlying economic cycle dynamics. Evaluation on the monthly M4 Competition data shows that STSA significantly outperforms Prophet and, while generally less accurate than stochastic trend models such as ARIMA, ETS, TBATS, and Theta, it produces superior forecasts for series with abrupt structural breaks where stochastic approaches struggle to adapt. Unlike traditional time series models, STSA offers an interpretable decomposition that reveals the causal narrative behind the series' evolution, enhancing the credibility of out-of-sample forecasts.