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

TL;DR

This study rigorously evaluates whether stationarity transformations genuinely improve time series forecast accuracy, revealing limited benefits except for variance stabilization, and emphasizing empirical testing over theoretical assumptions.

Contribution

It provides a comprehensive controlled experimental analysis showing that most stationarity transformations do not significantly enhance forecast accuracy, challenging common preprocessing practices.

Findings

Transformations improve forecasts only 18% of the time when matched to data properties.

Variance stabilization methods like log and Box-Cox improve accuracy in 60-65% of heteroscedastic cases.

Differencing linear-trend series worsens forecast accuracy across all tested scenarios.

Abstract

Stationarity transformations are standard preprocessing in time series forecasting, yet their actual impact on accuracy across different non-stationarity types and model families has received little controlled evaluation. We construct synthetic datasets with known properties - trend, seasonality, heteroscedasticity, and combinations - and apply fourteen transformation configurations across seven models and three forecast horizons (3,528 experiments). Stationarity is quantified via consensus ratios from ten statistical tests, and each transform-dataset pair is classified as matched or mismatched based on whether the transform targets the dataset's known non-stationarity. For matched pairs, transforms improve forecasts only 18% of the time. The primary exception is variance stabilization: log and Box-Cox on heteroscedastic data improve accuracy in 60-65% of cases. Differencing a linear-trend series - a textbook use case - worsens forecasts in all cases tested. Mediation analysis confirms that while transforms achieve trend stationarity, this does not translate into lower forecast error; the mechanism is signal attenuation. Real-world validation on TSA airport passenger data corroborates these findings. Our results suggest transformation selection should be guided by empirical out-of-sample evaluation rather than theoretical stationarity assumptions.