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

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

Problem Statement
Stationarity transformations (e.g., differencing, log transforms, seasonal adjustments) are a standard preprocessing step in time series forecasting, rooted in the assumption that many classical models (AR, ARMA) require stationary input to function correctly. However, there is a lack of controlled empirical evidence evaluating whether achieving stationarity through preprocessing actually improves forecast accuracy. Most existing studies either apply fixed pipelines without comparison or rely on real-world data where the true data-generating process (DGP) is unknown, making it impossible to determine if a transformation targets the correct form of non-stationarity. This study addresses the gap between theoretical preprocessing rationale and empirical forecast performance.

Methodology
The authors conducted a fully crossed factorial experiment involving 3,528 configurations:

• Datasets: 11 synthetic time series with known DGPs isolating specific non-stationarity patterns (linear trend, seasonality, heteroscedasticity, autoregressive structures, random walks, and combinations) and 1 real-world dataset (TSA Checkpoint Travel Numbers). Synthetic series were 200 observations long at weekly frequency.
• Transformations: 14 configurations were tested, including single transforms (none, first differencing, seasonal differencing, fractional differencing, log, Box-Cox) and pipeline combinations (e.g., log + difference).
• Models: 7 forecasting models spanning three categories: those traditionally assuming stationarity (AR, ARMA), those with partial stationarity handling (ARIMA), and those not requiring stationarity (ETS, Holt-Winters, Prophet, Gradient Boosting/LightGBM).
• Evaluation: Forecasts were generated for horizons of 4, 12, and 24 weeks. Accuracy was measured using Symmetric Mean Absolute Percentage Error (sMAPE) on the original scale (after inverse transformation).
• Stationarity Measurement: A consensus ratio derived from ten statistical tests (covering trend, variance, and seasonality) was used to quantify stationarity, with domain-specific exclusion rules to prevent spurious results.
• Analysis: The study employed mediation analysis to decompose the causal pathway: Transformation $\rightarrow$ Stationarity $\rightarrow$ Forecast Accuracy.

Key Results

1. General Degradation: Contrary to standard practice, applying stationarity transformations generally worsened forecast accuracy. Differencing-based transforms (first, seasonal, fractional) acted as high-pass filters, removing predictable low-frequency signals and significantly increasing sMAPE.
2. The Variance Stabilization Exception: The primary exception was variance stabilization (log and Box-Cox transforms). On heteroscedastic data, these transforms improved accuracy in 60–65% of cases by addressing modeling assumption violations without attenuating predictive signal structure.
3. Matched vs. Mismatched: Even when a transformation was "matched" to the known non-stationarity (e.g., differencing a linear trend), it improved forecasts only 18% of the time. In many "textbook" cases, such as differencing a linear-trend series, accuracy worsened in all tested cases because the predictable trend signal was removed.
4. Model Independence: The negative impact of differencing persisted across all model families, including AR and ARMA. Modern implementations of these models often include internal trend parameterization, reducing the practical necessity of external differencing.
5. Mediation Findings: Mediation analysis confirmed that while transformations successfully increased trend stationarity (Path A), higher trend stationarity was associated with worse forecast accuracy (Path B). The mechanism was identified as signal attenuation. Conversely, achieving variance stationarity was positively associated with improved accuracy.
6. Real-World Validation: Results on the TSA airport passenger data corroborated the synthetic findings. Differencing was the most harmful transform, while a combination of variance stabilization and seasonal adjustment yielded the best results.

Significance and Claims
The paper claims that the relationship between stationarity and forecast accuracy is more nuanced than conventional preprocessing pipelines assume. The authors argue that:

• Signal vs. Stationarity: Achieving statistical stationarity does not equate to improved forecastability. Transformations that remove non-stationarity often remove the learnable signal required for extrapolation.
• Empirical over Theoretical: Transformation selection should be guided by empirical out-of-sample evaluation rather than theoretical assumptions about stationarity.
• Selective Preprocessing: Practitioners should distinguish between signal-preserving transforms (variance stabilization) and signal-suppressing transforms (differencing). Differencing should be applied with caution rather than as a default step, while variance stabilization remains a robust strategy for heteroscedastic data.

The study concludes that while stationarity remains a fundamental theoretical property for inference and model stability, it is not a reliable proxy for maximizing out-of-sample predictive accuracy in modern forecasting pipelines.