Benchmarks in univariate time series forecasting: a historical and methodological review

Abstract This paper provides a comprehensive historical and methodological review of univariate time series forecasting from the second half of the 19th century to 2025, with specific emphasis on benchmark methods that have shaped forecasting practice across economics, finance, energy, and supply chain management. We trace the evolution from foundational probabilistic theory through adaptive exponential smoothing, the Box-Jenkins ARIMA methodology, nonparametric methods and contemporary hybrid and learning frameworks. Our focus is deliberately on simple, replicable, and computationally efficient methods that serve as essential baselines against which more complex approaches must be evaluated. The chronological taxonomy spans eight distinct eras: the pre-1930 foundations; the formative decade (1930–1940); the probabilistic foundations (1940–1949); the empirical shift (1950–1964); the algorithmic and computational expansion (1965–1979); the consolidation phase (1980–1999); the competition and automation era (2000–2019); and the most recent era (2020–2025) introducing hybrid and adaptive learning frameworks. This review is essential, both for tracing the historical roots of forecasting methods and for understanding the basic principles on which benchmark models are built: simplicity, parsimony, computational efficiency, transparency, and out-of-sample reliability. This review is addressed to a broad readership: academic researchers and early career scholars tracing the intellectual and methodological history of the field, practitioners seeking reliable and transparent methods for operational forecasting, and management mathematicians and quantitative analysts from cognate disciplines—operational research, decision analytics, and management science—for whom benchmark forecasting methods constitute an essential but underexplored toolkit. Benchmark forecasting methods are the foundation of modern predictive analytics.