The Characteristics of ARMA (ARIMA) Model and Some Key Points to Be Noted in Application: A Case Study of Changtan Reservoir, Zhejiang Province, China

Accurate water quality prediction is the basis for good water environment management and sustainable use of water resources. As an important time series forecasting model, the Autoregressive Moving Average Model (ARMA) plays a crucial role in environmental management and sustainability research. This study addresses the factors that affect the ARMA model’s forecast accuracy and goodness of fit. The research results show that the sample size used for model parameters estimation is the main influencing factor for the goodness of fit of an ARMA model, and the prediction time is the main factor affecting the prediction error of the model. Constructing a stable and reliable ARMA model requires a certain number of samples for the estimation of model parameters. However, using an excessive number of samples will not further improve the ARMA model’s goodness of fit but rather increase the workload and difficulty of data collection. The ARMA model is not suitable for long-term forecasting because the prediction error of ARMA models increases with the increase of prediction time, and when the prediction time exceeds a certain limit, the fitted values of an ARMA model will almost no longer change with the time, which means the model has lost its significance of prediction. For time series with periodic components, introducing periodic adjustment factors into the ARMA model can reduce the prediction error. These findings enable environmental managers and researchers to apply the ARMA model more rationally, hence developing more precise pollution control and sustainable development plans.