A0412
Title: Kullback-Leibler-based characterizations of score-driven updates
Authors: Ramon de Punder - University of Amsterdam (Netherlands) [presenting]
Abstract: Score-driven models have been applied in some 400 published articles over the last decade. Much of this literature cites the optimality result in a prior study, which, roughly, states that succinctly small score-driven updates are unique in locally reducing the Kullback-Leibler divergence relative to the true density for every observation. This is at odds with other well-known optimality results; the Kalman filter, for example, is optimal in a mean-squared-error sense, but occasionally moves away from the true state. It is shown that score-driven updates are, similarly, not guaranteed to improve the localized Kullback-Leibler divergence at every observation. The seemingly stronger result in the prior study is due to their use of an improper (localized) scoring rule. Even as a guaranteed improvement for every observation is unattainable, it is proven that succinctly small score-driven updates are unique in reducing the Kullback-Leibler divergence relative to the true density in expectation. This positive, albeit weaker, result justifies the continued use of score-driven models and places their information-theoretic properties on a solid footing.
