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Alessandra LUATI (University of Bologna) “On the optimality of score driven models”

June 1, 2023 @ 11:30 am - 12:30 pm

Finance & Financial Econometrics: 
Time: 11.30 am
Date: 1th of June 2023
Room 3001

Alessandra LUATI (University of Bologna) “On the optimality of score driven models”

Abstract :Score-driven models have been recently 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–Leibler divergence between the true conditional density and the postulated density of the model. A key limitation of such optimality property is that it holds only locally both in the parameter space and sample space, yielding to a definition of local Kullback–Leibler divergence that is in fact not adivergence measure. The current paper shows that score-driven updates satisfy stronger optimality properties that are based on a global definition of Kullback–Leibler divergence. In particular, it is shown thatscore-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 generalisation 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.
(Joint with Paolo Gorgi (VU Amsterdam) et Sacha Lauria (University of Bologna))