Optimal Weighted Markov Model and Markov Optimal Weighted Combination Model with Their Application in Hunan’s Gross Domestic Product

In this paper, we mainly establish an optimal weighted Markov model to predict the GDP of Hunan Province from 2017 to 2023. The new model is composed of a fractional grey model and a quadratic function regression model weighted combination and is obtained through Markov correction. First, the optimal order r of the fractional grey model (FGM) is determined by using the particle swarm optimization (PSO) algorithm, and the FGM model is established. Second, a quadratic regression model is established based on the scatter plot of the data. Then, the optimal weighted Markov model (OWMKM) is obtained by combining the above two sub-models (i.e., the optimal weighted combination model (OWM)) and using Markov correction. Finally, the new model is applied to estimate and predict the GDP of Hunan Province from 2017 to 2023. The forecast results show that the four statistical measures of the optimal weighted Markov model, such as MAPE, RMSE, R 2 , and STD, are superior to the optimal weighted combination model (OWM), the nonlinear auto regressive model (NAR) and the autoregressive integrated moving average model (ARIMA), which indicates that our new model has strong fitting and higher accuracy. We establish the quadratic regression Markov model (QFRMKM), the fractional grey Markov model (FGMKM), and the optimal combination model of these two sub-models (MKMOWM). The effects of the MKMOWM and OWMKM are compared. This research provides a scientifically reliable reference and has significant importance for understanding the development trends of the economy in Hunan Province, enabling governments and companies to make sound and reliable decisions and plans.