Multi-Scale Decomposition and Autocorrelation Modeling for Classical and Machine Learning-Based Time Series Forecasting

Environmental time series, such as near-surface air temperature, exhibit strong multi-scale structure and persistent autocorrelation. Accurate forecasting therefore requires careful consideration of both temporal scale separation and serial dependence. In this study, we evaluate a unified framework that integrates Kolmogorov–Zurbenko (KZ) filtering with two classes of models: (i) classical regression with Cochrane–Orcutt autocorrelation correction, and (ii) an autocorrelation-adjusted Long Short-Term Memory (LSTM) network that learns an embedded correlation coefficient (ρ). All models are assessed using standardized meteorological predictors of T2M under walk-forward validation. The LSTM trained on raw predictors shows moderate performance (RMSE = 0.73, R2=0.46, DW = 0.79), which improves after KZ filtering (RMSE = 0.59, R2=0.63, DW = 1.84). Classical regression applied to KZ-decomposed predictors and corrected using the Cochrane–Orcutt procedure achieves substantially higher accuracy (RMSE = 0.41, R2=0.89, DW ≈2.0), outperforming the LSTM in both predictive precision and residual behavior. Visual diagnostics further confirm tighter predicted–actual alignment and near-white residuals in the classical models, whereas the LSTM retains small systematic deviations even after filtering. Overall, the results demonstrate that addressing multi-scale structures and autocorrelation had a greater impact than increasing model complexity. Integrating spectral decomposition with autocorrelation correction thus produces more reliable, statistically valid forecasts, demonstrating that classical regression with KZ filtering can surpass LSTM models in both accuracy and interpretability. These findings emphasize the value of combining time series–aware pre-processing with both traditional and neural network approaches for environmental prediction.