Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/301121 
Year of Publication: 
2024
Series/Report no.: 
Tinbergen Institute Discussion Paper No. TI 2024-051/III
Publisher: 
Tinbergen Institute, Amsterdam and Rotterdam
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 Blasques et al. (2015), which, roughly, states that sufficiently small score-driven updates are unique in locally reducing the Kullback-Leibler (KL) 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 may move in the wrong direction for atypical observations. We show that score-driven filters are, similarly, not guaranteed to improve the localized KL divergence at every observation. The seemingly stronger result in Blasques et al. (2015) is due to their use of an improper (localized) scoring rule. Even as a guaranteed improvement for every observation is unattainable, we prove that sufficiently small score-driven updates are unique in reducing the KL divergence relative to the true density in expectation. This positive-albeit weaker- result justifies the continued use of score-driven models and places their informationtheoretic properties on solid footing.
Subjects: 
generalized autoregressive score (GAS)
dynamic conditional score (DCS)
Kullback Leibler
censoring
scoring rule
divergence
Document Type: 
Working Paper

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