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The continuous-time limit of score-driven volatility models

Buccheri, G., Corsi, F. ORCID: 0000-0003-2683-4479, Flandoli, F. & Livieri, G. (2021). The continuous-time limit of score-driven volatility models. Journal of Econometrics, 221(2), pp. 655-675. doi: 10.1016/j.jeconom.2020.07.042


We provide general conditions under which a class of discrete-time volatility models driven by the score of the conditional density converges in distribution to a stochastic differential equation as the interval between observations goes to zero. We show that the form of the diffusion limit depends on: (i) the link function, (ii) the conditional second moment of the score, (iii) the normalization of the score. Interestingly, the properties of the stochastic differential equation are strictly entangled with those of the discrete-time counterpart. Score-driven models with fat-tailed densities lead to continuous-time processes with finite volatility of volatility, as opposed to fat-tailed models with a GARCH update, for which the volatility of volatility is explosive. We examine in simulations the implications of such results on approximate estimation and filtering of diffusion processes. An extension to models with a time-varying conditional mean and to conditional covariance models is also developed.

Publication Type: Article
Additional Information: © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Publisher Keywords: Weak diffusion limits, Score-driven models, Student-t, General error distribution
Subjects: H Social Sciences > HB Economic Theory
Departments: School of Policy & Global Affairs > Economics
SWORD Depositor:
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