Research On Spatially Variable Coefficient Autoregressive Mode

When analyzing and modeling spatial data,its potential spatial characteristics should be fully considered to reflect the spatial patterns and relationships contained in the data.The two most frequently considered and important spatial features are spatial autocorrelation and spatial heterogeneity.In order to better consider spatial autocorrelation and spatial heterogeneity at the same time,this paper studies the spatial varying coefficient autoregressive model,in which the spatial lag coefficient and regression coefficient are set as spatial varying coefficients,which are nonparametric functions of spatial location.For the spatial varying coefficient autoregressive model,this paper proposes three estimation methods,which are:① estimation method based on two-stage least squares framework;② Based on local linear technology and local GMM method;③Considering the nonlinear relationship between endogenous variables and instrumental variables,an estimation method based on local linear GWR method is proposed.In this paper,the performance of the three kinds of estimation methods is investigated through numerical simulation.In the simulation,the parameters of the model are reasonably set,the root mean square error of parameter estimation is calculated,and the real surface of the parameters and the fitting diagram of the estimation are drawn,so that the effect of parameter estimation can be seen intuitively.Generally speaking,with the increase of sample size,the fitting accuracy of the three methods continues to improve.It can be reasonably speculated that the parameter estimation value will converge to the true value of the parameter with the increase of sample size.Comparing the estimation effects of the three methods,it can be found that the estimation method based on the two-stage least squares framework is relatively poor,and the estimation effect under the estimation methods of local GMM Estimation and local linear GWR method is better.In order to illustrate the flexibility and applicability of the spatial varying coefficient autoregressive model studied in this paper,the local GMM method of the spatial varying coefficient autoregressive model is taken as an example to compare its estimation effect with the geographic weighted regression model and the spatial autoregressive model.Generating data according to different model forms,it can be found that the estimation effect of spatial varying coefficient autoregressive model is the best,has wide adaptability,and is not prone to model setting errors.From the case study,combined with the spatial varying coefficient autoregressive model,this paper studies the impact of house price differences in 31 provinces and autonomous regions(excluding Taiwan,Hong Kong and Macao)on Residents’ consumption level in 2020.For the example studied,the three estimation methods proposed in this paper for spatial varying coefficient autoregressive model also have good estimation results.To sum up,the model studied in this paper can comprehensively consider spatial autocorrelation and spatial heterogeneity,and the numerical simulation and example analysis of the proposed research method confirm the effectiveness of the proposed method and has a wide application prospect.