On Optimality of Score Driven Models

Lauria, Christopher Sacha Aristide (2021) On Optimality of Score Driven Models, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Scienze statistiche, 33 Ciclo. DOI 10.6092/unibo/amsdottorato/9627.
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The contribution of this thesis consists in proving that score driven models possess a novel, intuitive, high dimensional and global optimality criterion, called Conditional Expected Variation optimality that formalizes the following words from Creal et al. (2013) "The use of the score is intuitive. It defines a steepest ascent direction for improving the model's local fit in terms of the likelihood or density at time t given the current position of the parameter. This provides the natural direction for updating the parameter. " Indeed, the fact that the score defines a steepest ascent direction is crucial in deriving the results and for the proposed optimality criterion to hold. To prove the aforementioned property, a point of contact between the econometric literature and the time varying optimization literature will be established. As a matter of fact, the Conditional Expected Variation optimality can be naturally viewed as a generalization of the monotonicity property of the gradient descent scheme. A number of implications on the specification of score driven models are analyzed and discussed, even in the case of model misspecification.

Tipologia del documento
Tesi di dottorato
Lauria, Christopher Sacha Aristide
Dottorato di ricerca
Settore disciplinare
Settore concorsuale
Parole chiave
Time varying parameters; Score functions; Gradient descent.
Data di discussione
23 Marzo 2021

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