Parameter Estimation And Application Of Two Combined Models

In this paper,we studied the parameter estimation of GM(1,1)model,log-linear model and Logistic population model,and based on the combination of parameter optimization GM(1,1)model and log-logarithmic model,Logistic model and linear model,we analyzed the trend and influencing factors of GDP and population change in Heilongjiang Province.The main content is divided into two parts.In the first part,given an analytic expression for the constant parameter term estimation.Numerical analysis shows that when the measurement error exists in the beginning and end data,the revised estimation based on the least absolute method is more accurate than the traditional estimation method.It also apply this model to the analysis of the GDP development trend and influencing factors of Heilongjiang Province.Firstly,set up a log-linear model.Since there is a polycollinearity among the fitting variables,Secondly,gaven the estimation of the parameters in the model.Considering the sustainable change of economic growth,then set up a combination model of GM(1,1)model with parameter optimization and double logarithm model.For the last step,The combination model not only contains the sustainable characteristics of economic development,but also includes the influence of other factors,so that the model has higher forecasting accuracy and clearly interpretation.In the second part,considered that GM(1,1)model is a differential equation model,and the double logarithmic model is a statistical model.In this part,first further explore the combination model of mechanism model and statistical model,and also take Heilongjiang population as the research object to study the advantages and disadvantages of this combination model.Next,taken the population of Heilongjiang Province as the dependent variable,established the Logistic population model,and estimated the parameters of the model based on the absolute method to predict the population.Logistic population model reflects the development regular pattern of the population itself.In order to consider the impact of other factors on the population of Heilongjiang Province,this paper completed the selection of variables affecting the population factors of Heilongjiang Province through Lasso regression,and we established a linear regression model contains the number of employed people and the regional gross domestic product.Finally,use Logistic population model and Lasso regression model to establish the combination model of parameter optimization,given the population prediction of Heilongjiang Province,and the comprehensive analysis of the influencing factors of population change in Heilongjiang Province.