Enhanced Bagging-Based Approach for Forecasting Nonstationary Time Series: Bridging Nonstationarity With a Scaled Logit Transformation

Abstract

Traditional block bootstrapping methods, such as the moving block bootstrap, can effectively preserve serial dependence within blocks when the underlying time series is stationary; however, when applied to nonstationary data, these methods often fail to capture evolving dependence structures, which can substantially undermine the performance of bagging predictors. This limitation highlights the need for effective strategies that transform nonstationary time series into stationary counterparts before bootstrapping, thereby enabling the reliable application of block bootstrapping in nonstationary settings. Motivated by this issue, this study develops an enhanced bagging-based approach incorporating a scaled logit transformation and a decomposition technique. In particular, the scaled logit transformation operates without parameter estimation and effectively stabilizes variance for data containing negative values or bounded ranges, such as proportions and rates, unlike a Box–Cox transformation, which relies on parameter estimation and requires positive data. The effectiveness of our method is examined through two illustrative studies: a simulation study and a real data analysis. In the simulation study, its performance is evaluated using various nonstationary time series generated under controlled conditions. For the real data analysis, three nonstationary time series datasets with different frequencies are utilized to substantiate its practical applicability.