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Accidents involving heavy metal pollution of water and the environment cause huge casualties and loss of property, making the monitoring of heavy metal pollution of great importance. In order to overcome the disadvantages of the traditional model algorithm, such as low predictive accuracy and poor fusion ability, a new combined forecasting model was developed based on the autoregressive integrated moving average model and grey theory. The autoregressive integrated moving average model time series forecasting methods were used to make a preliminary forecast for heavy metal historical data. Then a non-interval GM(1,1) model was built. The model residual of initial forecasts were put as the input of GM(1,1) to be modified. The non-interval GM(1,1) model is established regarding the residual value of the ARIMA. Finally, the initial forecasts of ARIMA model and the residual prediction value of GM(1, 1) fusion and combination forecast GM-ARIMA model were constructed. The heavy metals monitoring data of a river in Hebei province in 1978–2007 were taken as the sample to be analyzed. The predictive results of the autoregressive integrated moving average model, GM(1,1) model and the GM-ARIMA model are compared. The results show that the GM-ARIMA model has better predictive performance and fusion ability.
Energy is an important material basis for the economic development and social progress. Whether the energy supplies could support the sustainable economic growth of a country in the future is becoming an important problem in the world. The empirical mode decomposition (EMD) is a technique for decomposing a time series into a finite number of components referred to as intrinsic mode functions. This paper puts forward the EMD-GPM model integrating EMD and GPM for energy demand forecasting. In particular we use the increase of energy demand as the input of EMD. Different characteristics information of increase time series can be shown on different scales by EMD. Considering that grey system prediction model can reflect the general trends of change visually, and periodic extensional prediction model mainly reflects the periodic fluctuation, the grey-periodic extensional combinatorial model is adopted to predict the IMFs containing specific information. So, the EMD-GPM model considers both the development trends and periodic fluctuation of the energy demand.