{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T04:36:07Z","timestamp":1790138167216,"version":"4.0.1"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,11,9]],"date-time":"2023-11-09T00:00:00Z","timestamp":1699488000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,9,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Score-driven models have recently been introduced as a general framework to specify time-varying parameters of conditional densities. The score enjoys stochastic properties that make these models easy to implement and convenient to apply in several contexts, ranging from biostatistics to finance. Score-driven parameter updates have been shown to be optimal in terms of locally reducing a local version of the Kullback\u2013Leibler divergence between the true conditional density and the postulated density of the model. A key limitation of such an optimality property is that it holds only locally both in the parameter space and sample space, yielding to a definition of local Kullback\u2013Leibler divergence that is in fact not a divergence measure. The current paper shows that score-driven updates satisfy stronger optimality properties that are based on a global definition of Kullback\u2013Leibler divergence. In particular, it is shown that score-driven updates reduce the distance between the expected updated parameter and the pseudo-true parameter. Furthermore, depending on the conditional density and the scaling of the score, the optimality result can hold globally over the parameter space, which can be viewed as a generalization of the monotonicity property of the stochastic gradient descent scheme. Several examples illustrate how the results derived in the paper apply to specific models under different easy-to-check assumptions, and provide a formal method to select the link function and the scaling of the score.<\/jats:p>","DOI":"10.1093\/biomet\/asad067","type":"journal-article","created":{"date-parts":[[2023,11,7]],"date-time":"2023-11-07T08:58:13Z","timestamp":1699347493000},"page":"865-880","source":"Crossref","is-referenced-by-count":27,"title":["On the optimality of score-driven models"],"prefix":"10.1093","volume":"111","author":[{"given":"P","family":"Gorgi","sequence":"first","affiliation":[{"name":"Department of Econometrics and Data Science, Vrije Universiteit Amsterdam , De Boelelaan 1105 , 1081HV Amsterdam, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C S A","family":"Lauria","sequence":"additional","affiliation":[{"name":"Department of Statistical Sciences, University of Bologna , via Belle Arti 41 , Bologna 40126, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A","family":"Luati","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Imperial College London , 108 Queen\u2019s Gate , SW7 2AZ, London, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,11,9]]},"reference":[{"key":"2024090418514868600_asad067-B1","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/978-1-4612-1694-0_15","volume-title":"Selected Papers of Hirotugu Akaike","author":"Akaike","year":"1998"},{"key":"2024090418514868600_asad067-B2","doi-asserted-by":"publisher","DOI":"10.1080\/00036846.2023.2208335.","article-title":"Score function scaling for QAR plus Beta-t-EGARCH: an empirical application to the S&P 500","author":"Ayala","year":"2023","journal-title":"Appl. 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