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Title: Spatial heterogeneous 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)
Abstract: The traditional SARX models offer a simple way of capturing the essence of spatial interactions via the $Wy$ operator, but 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 captures for such non-linearities and unobserved heterogeneity by allowing for varying-coefficients in both the exogenous regressors coefficients and to the error term structure. The coefficients of the exogenous regressors are allowed to smoothly vary with location s (which s denotes the denotes the smoothing-parameter) and therefore enables us to introduce spatial trends/non-stationarity in $y$ or heterogeneous non-linearity between $X$ and $s$. We allow both the exogenous regressors and the innovation sequence to depend on location $s$ by defining them as unknown functions of this 2-dimensional vector. Following a set of assumptions, the unknown parameters are estimated by a profile maximum likelihood which is based on a two-step procedure where: 1. The unknown parameters are estimated at location $s$ by local maximum likelihood estimation (LMLE) for a given lambda, and 2. The the spatial profile likelihood can be defined from (1.) and the estimator of the spatial parameter is then defined as the maximum profile likelihood estimator (MPLE).