Grey extended prediction model based on IRLS and its application on smog pollution

Abstract

In recent years, smog weather in China has continued to worsen. Aiming at the problem of smog pollution prediction, a new grey extended prediction model, which is based on the GM (grey model) (1,1) model, is proposed in this paper. When the input function takes different forms, the grey extended model can degenerate into various existing grey prediction models. At the same time, the iterative reweighted least squares method (IRLS) is introduced to improve the models. In addition, to study the application effect of the grey extended prediction model GM(1,1,u(t)) and the iterative reweighted least squares method, based on the data of the air quality index (AQI) from December 2013 to February 2018, in Shanghai, four different forms of the GM(1,1,u(t)) model are established in this paper. The ordinary least square method (OLS) and the iterative reweighted least squares method are used to estimate the parameters, and the simulation and prediction results of the models are compared with those of the univariate linear regression model, the autoregressive integrated moving average (ARIMA) model and the feedforward neural network model. The result shows that the GM(1,1,u(t)) model (where u(t) = 1) under the IRLS method has the best prediction effect, which is not only suitable for predicting the normal values of AQI, but also suitable for predicting the outliers of AQI Therefore, it is proven that the GM(1,1,u(t)) model under iterative reweighted least squares is superior in simulation and prediction.