Do Stationarity Transformations Actually Improve Time Series Forecasts? A Controlled Experimental Evaluation

Stationarity transformations, such as differencing, are a common preprocessing step in forecasting, motivated by the idea that modifying a series to achieve stationarity improves accuracy.

Whether this is true, and for which processes, has rarely been evaluated in controlled experiments.

We study the decision to transform as the object of inquiry.

We cross eighteen synthetic data-generating processes, most of them stochastic-trend processes spanning exact and near unit roots, fractional integration, seasonal unit roots, structural breaks, and heteroscedasticity, with ten transformations, five models, and three horizons, replicated by Monte Carlo, for 35,099 evaluations.

Each forecast is inverted to the original scale, with the differencing inverse anchored at the forecast origin, and scored by the mean absolute scaled error.

Signal-preserving transforms, namely deterministic detrending and seasonal differencing matched to series structure, improve accuracy, whereas indiscriminate differencing degrades it.

A mediation analysis shows that differencing achieves trend stationarity, but trend stationarity is only weakly associated with accuracy, and transforms differ in their effects on predictable structure.

Choosing the transformation by out-of-sample validation yields lower regret than unit-root pretesting or any fixed rule, with blanket differencing performing the worst.

The findings are confirmed by real-world validation on nine series from two domains.