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The relationship between pollutant discharge and economic growth has been a major research focus in environmental economics. To accurately estimate the nonlinear change law of China's pollutant discharge with economic growth, this study establishes a transformed nonlinear grey multivariable (TNGM (1, N )) model based on the nonlinear least square (NLS) method. The Gauss-Seidel iterative algorithm was used to solve the parameters of the TNGM (1, N ) model based on the NLS basic principle. This algorithm improves the precision of the model by continuous iteration and constantly approximating the optimal regression coefficient of the nonlinear model. In our empirical analysis, the traditional grey multivariate model GM (1, N ) and the NLS-based TNGM (1, N ) models were respectively adopted to forecast and analyze the relationship among wastewater discharge per capita (WDPC), and per capita emissions of SO₂ and dust, alongside GDP per capita in China during the period 1996-2015. Results indicated that the NLS algorithm is able to effectively help the grey multivariable model identify the nonlinear relationship between pollutant discharge and economic growth. The results show that the NLS-based TNGM (1, N ) model presents greater precision when forecasting WDPC, SO₂ emissions and dust emissions per capita, compared to the traditional GM (1, N ) model; WDPC indicates a growing tendency aligned with the growth of GDP, while the per capita emissions of SO₂ and dust reduce accordingly.

The NLS-Based Nonlinear Grey Multivariate Model for Forecasting Pollutant Emissions in China