A Residual-Regulated Machine Learning Method for Non-Stationary Time Series Forecasting Using Second-Order Differencing

This study proposes a modeling method based on second-order differencing and residual regulation to address non-stationarity and noise in time series forecasting. Second-order differencing is first applied to weaken trend and seasonal components, making the data closer to a stationary state and providing stable inputs for subsequent modeling. On this basis, a residual regulation mechanism is introduced to dynamically incorporate prediction errors into model updates, reducing the negative impact of residual accumulation on stability. By combining linear regression with regularization, the method achieves parameter sparsity on differenced features, which enhances the characterization of key dynamic patterns while avoiding overfitting. Furthermore, a multi-step forecasting framework is constructed that considers both trends and fluctuations during recursive prediction, allowing the model to maintain high accuracy and robustness under complex conditions. Experiments conducted on the Kaggle retail transaction dataset include multidimensional comparative analysis, showing that the method outperforms baseline models in mean squared error, mean absolute error, mean absolute percentage error, and coefficient of determination. The results confirm its ability to capture both long-term trends and short-term fluctuations in retail transaction data. Graphical analysis further demonstrates that the proposed method fits well across different fluctuation ranges and remains consistent and reasonable even under abnormal volatility or extreme changes. In conclusion, the combination of second-order differencing and residual regulation provides a novel and effective solution for forecasting complex non-stationary time series and shows practical value in business data modeling tasks.