Estimation,Testing And Applications Of Spatiotemporal Data Semiparametric Regression Models

Spatiotemporal data is a spatial panel dataset that takes the effects of variables over time into account.The spatiotemporal data regression models consider not only spatial correlation but also serial correlation,which is a significant difference between spatiotemporal econometrics and spatial econometrics.Baltagi pointed out that panel data spatial regression model assumes that cross section at each time has the same regional effect,which cannot be satisfied in practical situation,such as in cross-regional investment,a certain period unobserved shock often affect behavioral relationships in future periods,and ignoring serial correlation may lead to ineffective regression estimates.Since beginning of this century,scholars have studied different forms of parametric regression models with space-time filters which are established by adding serial correlation to error component of spatial error model,and their theories and applications are vigorously enriched.In view that above models cannot capture the ubiquitous nonlinear characteristics of economic variables,this thesis establish two new kinds of models:fixed/random effects semiparametric regression models with separable space-time filters and fixed/random effects semiparametric regression models with nonseparable space-time filters.By combining ordinary semiparametric regression model with separable/nonseparable space-time filters,the models can simultaneously study linear and nonlinear effects of coveriates,spatial correlations of error components,serial correlations of error/remainder error components and individual effects.For the proposed models,we first study their profile quasi-maximum likelihood estimation methods and hypothesis testing methods,and then conduct systematic studies of the asymptotic properties and small sample performance for estimators and test statistics.Furthermore,we illustrate the proposed estimation and testing techniques by using real datasets.The research content and conclusions are summarized as follows:(1)Estimation and testing on fixed/random effects semiparametric regression models with separable space-time filters.Based on the spatiotemporal data parametric regression model,we propose new fixed effects semiparametric regression model with separable space-time filters and random effects semiparametric regression model with separable space-time filters.We first construct profile quasi-maximum likelihood estimation methods for models,and hypothesis testing statistics for nonparametric components;Secondly.asymptotic properties of estimators and asymptotic distributions of test statistics are proved;Then,Monte Carlo simulations are applied to investigate small sample performance of estimation and testing method.(2)Estimation and testing on fixed/random effects semiparametric regression model with nonseparable space-time filters.Based on the spatiotemporal data parametric regression model,we propose new fixed/random effects semiparametric regression model with nonseparable space-time filters.We first construct profile quasimaximum likelihood estimation methods for models,and hypothesis testing statistics for nonparametric components;Secondly,asymptotic properties of estimators and asymptotic distributions of hypothesis test statistics are proved;Then,Monte Carlo simulations are applied to investigate the small sample performance of estimation and testing method.(3)The studies on influencing factors of provincial housing price in China and Indonesian rice output by using theoretical research results.On the one hand,based on panel dataset from 2011-2018 of provincial housing price in China,we establish fixed effects semiparametric regression model with separable space-time filters and fixed effects semiparametric regression model with nonseparable space-time filters to describe the linear and nonlinear relationship of each variable on housing price.At the same time,the influence of spatial correlation and serial correlation in error component is investigated,and compared with the empirical results of other models.On the other hand,on the basis of Indonesian rice farm dataset,random effects semiparametric regression model with separable space-time filters and random effects semiparametric regression model with nonseparable space-time filters are applied to verify the existence of observable linear and nonlinear effects in data,as well as unobservable spatial and serial correlation.