Semi-parametric Temporal Data Model And Its Application

Statistical inference with spatio-temporal models is one of the mature and widely applied branches in statistics and econometrics. For a long time,howeve-r, its main theory is about the parametric models. Though standard spatial parametric models such as spatial lag models and spatial error models, may be useful for specification testing, they rely heavily on a parametric structure that is highly sensitive to model misspecification. Over the last two decades, with the improvement of computing facilities, some useful semiparametric modelling approaches have been proposed to capture the underlying relationships between responsevariables and their associated covariates, examples include geoadditive models, geographically weighted regression models, spatial nonparametric models.This thesis mainly discusses two type semiparaemtric spatio-temporal models. The first model is spatio-temporal additive model, which is an extension of geoadditive models and semiparametric spatial models. The second model is mixed geographically and temporally weighted regression models, which is an extension of geographically weighted regression models. It is studied form the following asppects.For the spatio-temporal additive model, we first develop a profile least-squares approach for the parametric and nonparametric component. Next, when some additional linear restrictions on the parametric component are available, we postulate a restricted profile least-squares estimator for the parameteric compon-ent. To check the validity of the linear constraints on the parametric component, and develop a test procedure for the validity of the linear constraints. Finally, some simulations are conducted to examine the performance of our proposed procedure and the results are satisfactory. Mixed geographically and temporally weighted regression model is a useful technique to explore spatial and temporally non-stationarity by allowing that some coefficients of the explanatory variables are constant and others are spatio-temporal varying, but its estimation and inference has not been systematically studied. We propose profile least-squares approach and backfitting method to es-timating the parametric component and spatio-temporal varying coefficients.