Score-Driven Modeling of Spatio-Temporal Data

• 成果类型: Article
• 署名作者: Gasperoni, Francesca; Luati, Alessandra; Paci, Lucia; D'Innocenzo, Enzo
• 署名单位: University of Cambridge; MRC Biostatistics Unit; University of Bologna; Catholic University of the Sacred Heart
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1970571
• 发表日期: 2023
• 页码: 1066-1077
• 关键词: spatial autoregressive models; maximum-likelihood-estimation; fmri; inference; connectivity; cortex; mri

摘要

A simultaneous autoregressive score-driven model with autoregressive disturbances is developed 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.