Spatial Panel Models With Spatial Heterogeneity Effects And Applied Research

Spatial effect is a common research content in statistics.Spatial effect is widely used in econometrics,financial engineering,social science and other fields.In many cases,there are response variables not only receiving the influence of explanatory variables,but also the relationship between different corresponding variables,Therefore,it is very important to consider spatial effect in modeling.Most of the existing researches on spatial effects only consider one spatial coefficient to describe spatial effects,which limits the description of spatial effects.This dissertation focuses on the research of heterogeneous spatial effects,and the main research content is composed of three parts:Heterogeneous spatial autoregressive model.In this paper,we propose a heterogeneous spatial autoregressive model(H-SAM),which can describe the spatial effects with the spatial coefficients of heterogeneity.We propose the conditional quasi maximum likelihood(QML)estimator and its calculation method,and prove the asymptotic properties of the estimator under a series of regular conditions.In advance,we relax some original assumptions,by changing the conditions,we can make the asymptotic behavior still satisfied,but the convergence rate is affected.Finally,we give three counter examples that the consistency is not satisfied.Heterogeneous arbitrage pricing model with heteroscedasticity.Based on the traditional arbitrage pricing theory(APT)model,we propose a heterogeneous spatial APT(HS-APT)model with heteroscedasticity,We use this model to analyze the stock index returns of 11 euro area countries,and find that there are heterogeneity spatial effects and heteroscedasticity in stock index returns.We also test the above two points and some other model hypotheses with hypothesis tests.Heterogeneous Spatial Lag Model.We propose a heterogeneous spatial lag model(H-SLM).We also give the QML estimator and calculation method of the model,and prove its asymptotic behavior under a series of regular conditions.We use H-SLM to analyse the air polution durning 228 countries in 30 province and autonomous region.It is found that the interaction of air pollution among different cities not only exists,but also takes the group(province)as the unit,and heteroscedasticity also exists,which also takes the group as the unit.We also use hypothesis test to prove that heterogeneity and heteroscedasticity are grouped.