Information-theoretic optimality of observation-driven time series models for continuous responses

Francisco Blasques (), Siem Jan Koopman and Andre Lucas

Biometrika, 2015, vol. 102, issue 2, 325-343

Abstract: We investigate information-theoretic optimality properties of the score function of the predictive likelihood as a device for updating a real-valued time-varying parameter in a univariate observation-driven model with continuous responses. We restrict our attention to models with updates of one lag order. The results provide theoretical justification for a class of score-driven models which includes the generalized autoregressive conditional heteroskedasticity model as a special case. Our main contribution is to show that only parameter updates based on the score will always reduce the local Kullback–Leibler divergence between the true conditional density and the model-implied conditional density. This result holds irrespective of the severity of model misspecification. We also show that use of the score leads to a considerably smaller global Kullback–Leibler divergence in empirically relevant settings. We illustrate the theory with an application to time-varying volatility models. We show that the reduction in Kullback–Leibler divergence across a range of different settings can be substantial compared to updates based on, for example, squared lagged observations.

Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (94)

Downloads: (external link)
http://hdl.handle.net/10.1093/biomet/asu076 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:102:y:2015:i:2:p:325-343.

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Biometrika is currently edited by Paul Fearnhead

More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK.
Bibliographic data for series maintained by Oxford University Press ().