Estimation for semiparametric nonlinear regression of irregularly located spatial time-series data

Large spatial time-series data with complex structures collected at irregularly spaced sampling locations are prevalent in a wide range of applications. However, econometric and statistical methodology for nonlinear modeling and analysis of such data remains rare. Asemiparametric nonlinear regression is thus proposed for modelling nonlinear relationship between response and covariates, which is location-based and considers both temporal-lag and spatial-neighbouring effects, allowing data-generating process nonstationary over space (butturned into stationary series along time) while the sampling spatial grids can be irregular. A semiparametric method for estimation is also developed that is computationally feasible and thus enables application in practice. Asymptotic properties of the proposed estimators are established while numerical simulations are carried for comparisons between estimates before and after spatial smoothing. Empirical application to investigation of housing prices in relation to interest rates in the United States is demonstrated, with a nonlinear threshold structure identified

On a semiparametric data-driven nonlinear model with penalized spatio-temporal lag interactions

To study possibly nonlinear relationship between housing price index and consumer price index for individual states in the US, accounting for the temporal lag interactions of the housing price in a given state and spatio-temporal lag interactions between states could improve the accuracy of estimation and forecasting. There lacks, however, methodology to objectively identify andestimate such spatio-temporal lag interactions. In this paper, we propose a semiparametric data-driven nonlinear time series regression method that accounts for lag interactions across space and over time. A penalized procedure utilizing adaptive Lasso is developed for the identification and estimation of important spatio-temporal lag interactions. Theoretical properties for our proposed methodology are established under a general near epoch dependence structure and thus the results can be applied to a variety of linear and nonlinear time series processes. For illustration, we analyze the US housing price data and demonstrate substantial improvement in forecasting via the identification of nonlinear relationship between housing price index and consumer price index aswell as spatio-temporal lag interactions