Random Compression Method And Its Application In Economic Model Dimension Reduction

In the research of economic system,the interaction of multiple time series is often involved.The increase of the number of variables and the number of lag periods is easy to cause "dimension disaster".The existing solutions,such as model shrinkage method according to AIC and BIC standards,prior variable selection method or factor analysis method,have certain defects.The first is to make the original model modified to facilitate parameter estimation and deviate from the original model setting,which leads to inaccurate parameter estimation and result prediction.Secondly,it is not easy to calculate the AIC or BIC of some complex models,such as quantile related models,because it is difficult to find the global optimal solution to the optimization problem of the objective function when there are many parameters,and the AIC and BIC values calculated based on the local optimal solution are not reliable.Aiming at the problem that it is difficult to estimate the high-dimensional economic model,this paper summarizes and proposes an alternative dimension reduction scheme-random compression method,and developed respectively the specific implementation steps of the random compression method in the quantile vector auto regression model and the quantile non parameter model.Both the numerical simulation and the actual data test show that the method performs well in the prediction of financial risks and the fitting of the non-linear economic model,especially in the model containing potential variables,such as the quantile model.Finally,this method is applied to the empirical analysis of the influencing factors model of house prices.The actual economic data is complex and changeable,and the random error terms often do not meet the normal distribution.In this paper,under a more robust quantile framework,we studied the practicability of the method of reducing dimensions by random compression,and developed a model dimension reduction method containing potential variables.The main work and innovation of this paper are as follows:1.the estimation steps of the random compression method of the multiple quantile vector auto regression model are given to solve the problem that the previous model cannot be estimated when it involves multiple and multi period lag.The accuracy of the method to the quantile prediction is verified by the numerical model and the actual data,which is of great significance to the short-term financial risk prediction and the prevention and resolution of financial risks.2.the estimation steps of the random compression method for the multi quantile non parameter model are given,and the best model fitting is obtained by selecting the best number and location of nodes more accurately.This method not only has a high precision of fitting,but also can obtain the non-linear relationship between variables at the quantiles in the empirical research of economic problems,and capture more detailed information.Subsequently,the research on the influence of per capita disposable income,interest rate and other variables on different housing prices proves this point.Based on the random projection method and the model average method,the random compression dimension reduction method proposed in this paper bypasses the estimation of the original parameters,and can more accurately fit and predict.It has great application value in preventing financial risks,testing financial theory and other economic problems including high-dimensional parameters.