Hybrid ARIMAX model integrating optimal time-lag selection and markov chain error correction for residential heating load forecasting

optimal control of heating systems. Existing approaches often assume uniform action times for multivariate features during the heating process and rely solely on complex neural-network models to mitigate lag effects in prediction, which substantially constrains model performance. To address this issue, an Optimal Time-Lag selection method (OTL) is proposed and integrated with an autoregressive integrated moving-average model with exogenous variables (ARIMAX) and a Markov chain for heating-load forecasting. The method adaptively selects the optimal time-lag steps for different categories of features via OTL, performs load prediction using the ARIMAX model, and finally constructs a residual state space with a Markov chain for error correction, thereby achieving more effective performance. The evaluation is conducted using daily data from a residential community in Dalian, Liaoning Province. Compared with the baseline model, the proposed approach achieves the best performance on the test set, with mean squared error (MSE) reduced by 94.41 %, mean absolute error (MAE) reduced by 82.65 %, root mean squared error (RMSE) reduced by 68.90 %, mean absolute percentage error (MAPE) decreased by 4.15 %age points, and the coefficient of determination (R²) increased by 5.84 %. These results indicate that the hybrid model effectively overcomes lag effects in load forecasting under limited sample sizes and daily-scale decision scenarios, providing reliable support for optimal scheduling and energy-saving control of district heating systems. • Proposes an optimal time-lag selection (OTL) method to address lag effects in heating-load forecasting. • Integrates OTL with ARIMAX and Markov chain models, markedly improving forecasting accuracy. • The hybrid model outperforms the baseline: MSE reduced by 94.4 %, MAE by 82.7 %, RMSE by 68.9 %, MAPE by 4.2 %age points, and R² improved by 5.8 %.