Score driven time-series modeling: progress, open ends, and recent applications

Professor André Lucas is Professor of Financial Econometrics at Vrije Universiteit Amsterdam and Research Fellow at the Tinbergen Institute. He received his Ph.D. in Econometrics from Erasmus University Rotterdam in 1996 and has held several academic leadership positions at VU Amsterdam and the Tinbergen Institute, including Director of Graduate Studies in Finance, Program Director of Risk Management, and Vice Dean of Research. His research focuses on financial econometrics, risk, and asset management, with particular interests in model instability, time-varying parameters, systemic risk, and score-driven models. He has published extensively in Econometrics and Statistics. He is also the recipient of the prestigious NWO VICI grant and previously served as Associate Editor of the Journal of Financial Econometrics. 

Score-driven (GAS) time-series models provide a unified observation-driven framework in which time-varying parameters evolve according to the scaled score of the conditional likelihood. This talk reviews the core methodology and its key asymptotic challenges, including consistency and asymptotic normality under misspecification, stability and ergodicity of the filter, and identification issues. It also highlights open problems such as extending the theory to high-dimensional settings, developing robust score updates, and clarifying links to optimal filtering in nonlinear state space models. Recent advances include connections to the optimization literature (such as implicit score models) and non-likelihood based criteria (such as proper scoring rules). Recent applications to dependence modeling, extremes and tail risk dynamics, tensor count data modeling, and time-varying multi-dimensional curve modeling are used as illustrations.