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Monthly electricity demand exhibits both persistent upward trends and recurring seasonal patterns, which together pose major obstacles to reliable forecasting. This research, therefore, introduces a single-variable time-series prediction strategy that uses the Hodrick-Prescott (HP) filter to decompose the demand sequence into a smooth trend component and a seasonal component. The trend is modeled using an autoregressive integrated moving-average (ARIMA) model, while recurrent neural networks (RNNs) are employed to capture recurring seasonal behavior. The complete forecast results from combining the two separate predictions. Model effectiveness is tested on Guangzhou’s monthly total electricity usage records. When benchmarked against established techniques, including Holt-Winters, Seasonal ARIMA, and error-trend-seasonal (ETS), the developed HP_RNN_ARIMA combined approach lowers mean absolute percentage error (MAPE), root mean square error (RMSE), and mean absolute error (MAE) in the ranges of approximately 9.70% to 35.66%, 14.18% to 35.06%, and 20.01% to 41.92%, respectively. Compared with individual neural network models such as backpropagation (BP), RNNs, and long short-term memory (LSTM), the new model reduces MAPE, RMSE, and MAE by 9.05%-44.02%, 20.88%-51.74%, and 29.53%-56.23%, respectively. Compared with alternative hybrid techniques, the reductions in these error measures range from 3.60% to 33.39%, 4.27% to 36.67%, and 4.43% to 44.87%. The model also attains the best scores on Willmott’s index (WI) and Legates and McCabe’s index (LMI), demonstrating stronger agreement with observed values. Overall, decomposing the series with the HP filter and modeling the resulting components independently yields a clear improvement in forecast quality.