On Semiparametrically Dynamic Functional-coefficient Autoregressive Spatio-Temporal Models with Irregular Location Wide Nonstationarity

Nonlinear dynamic modelling of spatio-temporal data is often a challenge, especially due to irregularly observed locations and location-wide non-stationarity. In this paper we propose a semiparametric family of Dynamic Functional-coefficient Autoregressive Spatio-Temporal (DyFAST) models to address the difficulties. We specify the autoregressive smoothing coefficients depending dynamically on both a concerned regime and location so that the models can characterise not only the dynamic regime-switching nature but also the location-wide non-stationarity in real data. Different smoothing schemes are then proposed to model the dynamic neighbouring-time interaction effects with irregular locations incorporated by (spatial) weight matrices. The first scheme popular in econometrics supposes that the weight matrix is pre-specified. We show that locally optimal bandwidths by a greedy idea popular in machine learning should be cautiously applied. Moreover, many weight matrices can be generated differently by data location features. Model selection is popular, but may suffer from loss of different candidate features. Our second scheme is thus to suggest a weight matrix fusion to let data combine or select the candidates with estimation done simultaneously. Both theoretical properties and Monte Carlo simulations are investigated. The empirical application to an EU energy market dataset further demonstrates the usefulness of our DyFAST models.