ARIMA Markov Model and Its Application of China’s Total Energy Consumption

We propose an auto regressive integrated moving average Markov model (ARIMAMKM) for predicting annual energy consumption in China and enhancing the accuracy of energy consumption forecasts. This novel model extends the traditional auto regressive integrated moving average (ARIMA( p , d , q )) model. The stationarity of China’s energy consumption data from 2000 to 2018 is assessed, with an augmented Dickey–Fuller (ADF) test conducted on the d -order difference series. Based on the auto correlation function (ACF) and partial auto correlation function (PACF) plots of the difference time series, the optimal parameters p and q are selected using the Akaike information criterion (AIC) and Bayesian information criterion (BIC), thereby determining the specific ARIMA configuration. By simulating real values using the ARIMA model and calculating relative errors, the estimated values are categorized into states. These states are then combined with a Markov transition probability matrix to determine the final predicted values. The ARIMAMKM model is validated using China’s energy consumption data, achieving high prediction accuracy as evidenced by metrics such as mean absolute percentage error (MAPE), root mean square error (RMSE), S T D , and R 2 . Comparative analysis demonstrates that the ARIMAMKM model outperforms five other competitive models: the grey model (GM(1,1)), ARIMA(0,4,2), quadratic function model (QFM), nonlinear auto regressive neural network (NAR), and fractional grey model (FGM(1,1)) in terms of fitting performance. Additionally, the model is applied to Guangdong province’s resident population data to further verify its validity and practicality.