Study On Growth Factors Of GDP In Guangxi Based On MCMC Principal Component Regression

As an important index to measure the economic development status and economic strength of a country or region,GDP has been the focus of researchers in various industries for many years.Through literature review,it is found that some scholars use time series method to study single variable GDP,some scholars use some commonly used regression methods to study GDP,and some scholars use grey forecasting method or combination model to study GDP,but there is no literature using principal component analysis method to study the coordination of GDP economic development.Moreover,there are few papers on the application of MCMC principal component regression method to predict GDP economic development.Therefore,this paper will establish a coordinated evaluation model and MCMC principal component regression prediction model for the economic development data of Guangxi,and analyze the economic development of Guangxi.This paper chooses the GDP data of Guangxi from 2000 to 2017 as the explanatory variable,and the data of fiscal revenue,total fixed asset investment,total industrial output and total import and export as the explanatory variable.Firstly,the coordination variable is determined and the coordination evaluation model is established;Secondly,the original variables are modeled by common principal component regression and MCMC principal component regression,and the parameters of MCMC principal component regression model are estimated by Gibbs sampling method;Finally,the two models are compared.Specific contents are as follows:First,the coordination evaluation model.Based on the economic data of Guangxi from 2000to 2017,this paper establishes a coordinated evaluation model to evaluate the economic growth of GDP in each year.The results show that:From 2000 to 2004,the growth period was slightly slow,from 2005 to 2011 was normal,from 2012 to 2015 was slightly fast,but in 2016 it suddenly turned into a slightly slow growth period,and returned to the normal growth period in2017.These coordination evaluations are more in line with the actual economic development situation,so it is effective to use this method to evaluate the coordination of economic development.Second,the general principal component prediction model and MCMC principal component prediction model.According to the correlation coefficient matrix of each explanatory variable,it can be seen that there is a strong correlation between each explanatory variable.Two modeling methods,common principal component regression and MCMC principal component regression,are selected to model the original variable,and Gibbs sampling method is used to estimate the parameters of MCMC principal component regression model.The results show that the coefficients of each explanatory variable in the regression model established by these two methods are positive,which is consistent with the economic significance of reality.By testing the general principal component regression model,the model passed the F test,and R~2 exceeded99%.Both models can effectively overcome the multi-collinearity between explanatory variables,and the results of the models are good.The third is the comparison of the two prediction models.The above two models are used to forecast the three years from 2015 to 2018,and the root mean square error is used to compare the advantages and disadvantages of the two models.The results show that the root mean square error of MCMC principal component regression method is 451.3475,and that of ordinary principal component regression method is 807.7472.That is to say,the modeling result of MCMC principal component regression method is better than that of ordinary principal component regression method.