The Paper titled “Score-Driven Modeling of Spatio-Temporal Data” that I have co-authored with Francesca Gasperoni, Alessandra Luati and Lucia Paci has been accepted for publication on the Journal of the American Statistical Association (JASA). You’ll find the abstract below and also a link to the full paper. You are also very welcome to let us know what you think about our work in the comments.
We developed a simultaneous autoregressive score-driven model with autoregressive disturbances for spatio-temporal data that may exhibit heavy tails. The model specification rests on a signal plus noise decomposition of a spatially filtered process, where the signal can be approximated by a nonlinear function of the past variables and a set of explanatory variables, while the noise follows a multivariate Student-t distribution. The key feature of the model is that the dynamics of the space-time varying signal are driven by the score of the conditional likelihood function. When the distribution is heavy-tailed, the score provides a robust update of the space-time varying location. Consistency and asymptotic normality of maximum likelihood estimators are derived along with the stochastic properties of the model. The motivating application of the proposed model comes from brain scans recorded through functional magnetic resonance imaging when subjects are at rest and not expected to react to any controlled stimulus. We identify spontaneous activations in brain regions as extreme values of a possibly heavy-tailed distribution, by accounting for spatial and temporal dependence.
Gasperoni, F., Luati, A., Paci, L., & D’Innocenzo, E. (2021). Score-Driven Modeling of Spatio-Temporal Data. Journal of the American Statistical Association, 1-12.