Buccheri, Giuseppe, Corsi, Fulvio, Flandoli, Franco and Livieri, Giulia 
ORCID: 0000-0002-3777-7329
(2021)
The continuous-time limit of score-driven volatility models.
Journal of Econometrics, 221 (2).
pp. 655-675.
ISSN 0304-4076
Abstract
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.
| Item Type: | Article |
|---|---|
| Official URL: | https://www.sciencedirect.com/journal/journal-of-e... |
| Additional Information: | © 2020 Elsevier B.V. |
| Divisions: | LSE |
| Subjects: | H Social Sciences > HB Economic Theory |
| Date Deposited: | 25 Jun 2024 16:39 |
| Last Modified: | 20 Dec 2024 00:55 |
| URI: | http://eprints.lse.ac.uk/id/eprint/123979 |
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