Effectiveness of un-decimated wavelet transform in time-series forecasting: A PV power calculation case study in BTU

This study explored the effectiveness of Un-Decimated Wavelet Transform (UWT) in time-series applications, using photovoltaic (PV) calculation as a case study. Real-time measurements of irradiance, ambient temperature, module temperature, and humidity were collected at 5-min intervals from a 1.2 kW rooftop PV system at Bursa Technical University. Wavelet-based features extracted with both UWT and the conventional Discrete Wavelet Transform (DWT) were combined with regression and tree-based learners to build 16 hybrid models. The results show that the shift-invariant UWT significantly improves both feature extraction and prediction accuracy compared to the DWT approach. The UWT–DT model achieved the highest accuracy, with the lowest MSE (0.0001), the lowest RMSE (0.0118) and the highest R² coefficient (0.9986). A Wilcoxon signed-rank test applied to paired RMSE values confirmed that these improvements were statistically significant ($p$ value < 0.05 for UWT-DT vs DWT-DT). In terms of computational complexity, the 'à trous' algorithm used in UWT requires convolution operations at every level, resulting in higher processing costs than DWT (12 ms feature extraction per 1024-sample input). However, the full-resolution features provided by UWT significantly reduced the error rates of tree-based models, raising R² above 0.99.