A hybrid monthly electricity demand forecasting model combining an Hodrick-Prescott filter, recurrent neural networks, and autoregressive integrated moving average

• A monthly electricity demand forecasting model combining HP filters, ARIMA, and RNNs. • The predictive accuracy of the model exceeds that of traditional time series methods. • The predictive accuracy the model exceeds that of individual BPs, RNNs, and LSTMs. • The model exhibits superior predictive performance relative to several hybrid models. • Applying the HP filter to decompose time series data improves predictive accuracy. The coexistence of growth trends and seasonal fluctuations in monthly electricity demand presents significant forecasting challenges. Therefore, this study proposes a univariate time series forecasting approach that applies the Hodrick-Prescott (HP) filter to decompose the demand series into trend and seasonal components. Autoregressive integrated moving average (ARIMA) is used to forecast the trend, while recurrent neural networks (RNNs) handle the periodic component. The final prediction is obtained by combining the forecasts of both components. The model’s predictive performance is evaluated using Guangzhou’s total electricity consumption data. Compared to traditional methods such as Holt-Winters, Seasonal ARIMA, and error-trend-seasonal (ETS), the proposed HP_RNN_ARIMA hybrid model reduces mean absolute percentage error (MAPE), root mean square error (RMSE), and mean absolute error (MAE) by approximately 9.70% to 35.66%, 14.18% to 35.06%, and 20.01% to 41.92%, respectively. Compared to standalone neural networks such as backpropagation (BP), RNNs, and long short-term memory (LSTM), the proposed model lowers MAPE, RMSE, and MAE by approximately 9.05% to 44.02%, 20.88% to 51.74%, and 29.53% to 56.23%, respectively. Against other hybrid models, it reduces these metrics by 3.60% to 33.39%, 4.27% to 36.67%, and 4.43% to 44.87%. It also achieves the highest Willmott’s index (WI) and Legates and McCabe’s index (LMI) scores, reflecting superior model fit. Moreover, applying the HP filter for decomposition and modeling each component individually significantly improves forecasting accuracy.