A Hybrid Wavelet–SARIMA–NARNN Model for Time Series Forecasting

This research aims to develop a hybrid forecasting framework to improve the accuracy of time series models by integrating Wavelet Transform with Seasonal Autoregressive Integrated Moving Average (SARIMA) and Nonlinear Autoregressive Neural Networks (NARNN). The proposed method relies on using wavelet shrinkage techniques to remove noise from time series data before applying the forecasting models. Several families of wavelets, such as Daubechies, Coiflets, and Symlets, were tested along with different threshold estimation methods like Universal, Minimax, and SURE to select the best model configuration. The methodology was applied to real data representing the maximum monthly electricity demand in the Kurdistan region of Iraq for the period (2014–2024). Simulation experiments were also conducted using data generated from the SARIMA model, with 250 repetitions for each case. The results showed that the proposed hybrid models (Wavelet-SARIMA and Wavelet-NARNN) clearly outperformed the traditional models in terms of accuracy metrics RMSE, MAE, and MAPE, confirming the effectiveness of wavelet integration in improving forecasting accuracy in time series analysis. The researchers conducted all analyses through MATLAB software.