Abstract

A simultaneous autoregressive score driven model is developed for spatio-temporal data that are generated by a multivariate Student-t distribution. The model specification rests on a signal plus noise decomposition of a spatially filtered process, where the signal can be approximated by a non linear function of the past variables and the noise follows a 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.

Joint work with: Francesca Gasperoni (University of Cambridge), Lucia Paci (University of Milano CSC ), Enzo D’Innocenzo (University of Bologna)