Test Of Structural Change Under Quantile Regression Model And Its Application

Test model structural breaks have drawn much attention from scholars both at home and abroad in the economic theory and application.There are many documents about the stability of the test model,but most of them are studied under the least square method.If there is a structural mutation in the model,this mutation occurs at the tail of the conditional distribution rather than near the center of the conditional distribution,especially when the distribution is thick tail,and the structural mutation test under the traditional least square method may fail.Because the traditional least squares regression curve only gives the model in the mean sense,just using a regression curve to estimate and explain the relationship between variables,just as an average to describe the distribution.While quantile regression considers the relationship between variables at different quantile levels,it uses a cluster regression curve to explain and estimate the model,so to test whether there is a structural mutation in the quantile regression under the quantile regression,A complete model structure of the mutation view.In this paper,starting from a simple linear regression,the estimated regression coefficients are expressed as follows:（?）～E(β_x),that is,the regression coefficient of the ordinary least squares method isessentially the result of weighted average of each coefficient in the region,where  are the center,and the entire sample area is the bandwidth,and using the Epanechnikov kernel function.In this sense,the parameter estimation is actually a special form of non-parametric estimation.For quantile regression,in smaller areas,the coefficients are expressed as a weighted average of the coefficients for each subdivision.Secondly,the test method for structural change under regression model is discussed.Whether it is ordinary least squares regression or quantile regression,the key to test whether structural mutations occur in the estimated coefficients lies in verifying whether the normal equations are consistent or not.Therefore,under the guidance of the idea of mutation detection of linear regression,this paper studies singlestructure mutation test in quantile regression:recursive test,Wald test,LR test,residual test（KS）and estimated coefficient test（FL）,and given the limit distribution of these test statistic,at the same time,the Monte Carlo simulation is carried out,the simulation data are generated under the null hypothesis,the empirical test level of these test statistic is analyzed,and the simulation is also made under the alternative hypothesisto investigate their test efficacy,The results of the analysis show that there is a difference between the test efficacy of these statistics and the breakpointlocation,residual distribution,breakpoint deviation,model form,quantile position and sample size and other factors are closely linked.Finally,based on the single structure mutation test,we also study several multi-structure change test methods under the regression of quantile:sequential test,Wald test and MDL test.Finally,on the basis of quantile regression theory and Granger causality test,this paper discusses the causal relationship between daily financing growth rate and daily return rate.The conclusion shows that the daily financing growth and The daily yield has a oneway causal relationship.The daily yield has an unstable causal relationship with the daily financing growth.The increase in the index and the decline in the index have inconsistent effects on financing.On the basis of quantile regression and structural break theory,the relationship between the trading volume and price in the two markets of Shanghai and Shenzhen was analyzed.The empirical results show that the relationship between volume and price in the Shanghai and Shenzhen markets is significant on relativelyhigh quantile,both of which are expressed as positive correlations between“volume rise and price increase”and“volume reduction and price decline”;On relatively low quantiles,the two showed a negative correlation.Due to the opening of the GEM and IPO of China Petroleum,the structural changes in the volume and price relations between the Shanghai and Shenzhen markets have mainly occurred in the relatively high trading volume,and the degree of influence on the Shenzhen market has been greater than that of the Shanghai stock market.