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Title: Spatial heterogenous autoregression with varying-coefficient covariate effects Authors:  Maria Kyriacou - University of Southampton (United Kingdom) [presenting]
Zudi Lu - University of Southampton (United Kingdom)
Peter CB Phillips - Yale University (United States)
Xiaohang Ren - University of Southampton (United Kingdom)
Abstract: The traditional SARX models offer a simple way of capturing spatial interactions. Still, they have been subject to criticism owing to their several limitations, including their inability to capture spatial non-linearities and unobserved heterogeneity. We propose a spatial heterogeneous autoregressive exogenous (SHARX) model which captures for non-linearities and unobserved heterogeneity via allowing for varying-coefficients in the coefficients of the exogenous regressors ($X$) and the error term. The coefficients of the exogenous regressors are allowed to vary with location ($s$) smoothly and therefore allows to introduce spatial trends in $y$ or heterogeneous non-linearity between $X$ and $s$. Under a set of assumptions, the unknown parameters are then estimated by a profile maximum likelihood-based on a two-step procedure. First, the unknown parameters are estimated at s by local maximum likelihood estimation for a given lambda. Then the spatial profile likelihood can be defined from step 1, and the estimator of the spatial parameter is then defined as the maximum profile likelihood estimator. We assess the performance of our estimators alongside the conventional ML and GMM methods via a simulation study and an empirical application using energy data from China.