Correlation Analysis Of Macroeconomic Variables Based On Graphical Modelling

As the data dimension continues to increase,traditional correlation analysis methods have great limitations for dealing with problems in high-dimensional situations.The Lasso method compresses the coefficients by constructing a penalty function,setting some coefficients to zero,and obtaining a more refined model.The graphical modelling graphically maps the relationships between variables and combines the probabilistic approach to solve complex model creation and analysis problems.The Gauss graphical modelling is a probability graphical modelling in which random variables obey Gaussian distribution.The lasso method combining the lasso method and the graphical modelling can quickly estimate the precision matrix based on the norm minimization method,and control the sparsity of the precision matrix by adjusting the penalty parameters,and can reduce the model while passing the graph.Simple and clear representation of complex models is a powerful way to handle complex high-dimensional data.When dealing with heterogeneous data with classification features,the graph lasoo method ignores the common information between categories when independently estimating the precision matrix.The multi-graph joint estimation method avoids the loss of common information between categories by stratified penalty constraint and the two coefficients compression of the groups lasso and lasso,while maintaining the common structure while allowing the existence of differences between categories.In this paper,the lasso method and the multi-graph joint estimation method are applied to the macroeconomic field.By constructing the sparse Gauss graphical modelling,the correlation between the 16 macroeconomic correlation variables in the country is analyzed,and 13 provinces and cities are further explored.Based on the correlation between economic variables,a multi-graph joint model of five provinces and cities with different economic development levels was constructed,and the public structure information between economically relevant variables of each group of provinces and cities was analyzed.The results show that among the 16 macroeconomic variables in the country,the number of variables related to financial,fiscal,foreign economic,real estate and fixed asset investment variables is the largest,while the number of variables related to the variables of national economy is the least.The macroeconomic related variables mostly exhibit non-intuitive correlations with the variables of the national economy;through the analysis of the multi-graph joint model of the five provinces and cities,and the comparative analysis with the separate estimation graphical modelling,the multi-graph joint model The public structure of different groups has been maintained,and the correlations between fiscal budgets and expenditures,and the total output value of agriculture,forestry,animal husbandry and fishery exist in different provinces and cities at different levels of economic development.