Maximum Likelihood Estimation for Generalized Autoregressive Score Models

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractThe strong consistency and asymptotic normality of the maximum likelihood estimator in observation-driven models usually requires the study of the model both as a filter for the time-varying parameter and as a data generating process (DGP) for observed data. The probabilistic properties of the filter can be substantially different from those of the DGP. This difference is particularly relevant for recently developed time varying parameter models. We establish new conditions under which the dynamic properties of the true time varying parameter as well as of its filtered counterpart are both well-behaved and We only require the verification of one rather than two sets of conditions. In particular, we formulate conditions under which the (local) invertibility of the model follows directly from the stable behavior of the true time varying parameter. We use these results to prove the local strong consistency and asymptotic normality of the maximum likelihood estimator. To illustrate the results, we apply the theory to a number of empirically relevant models.

Spillover dynamics for systemic risk measurement using spatial financial time series models

“…The current conditions extend those of Blasques et al (2014b) by accounting for the presence of exogenous variables X t in the model.…”

“…This illustrates that policies by regulators have at least been partly effective in breaking the high spill-over effects prevalent during the height of the European sovereign debt crisis. The lines of proof adopted here closely follow the original lines of proof in Blasques et al (2014b), extended to the case of exogenous variables.…”

“…The expressions may seem complicated at first, but we show below that their verification is often straightforward; see also Blasques et al (2014b) THEOREM 4. (Asymptotic Normality) Let {y t } t∈Z and {X t } t∈Z be SE sequences satisfying E|y t | Ny < ∞ and E|X t | Nx < ∞ for some N y > 0 and N x > 0 and let Assumptions 1-4 hold.…”

“…The moment conditions in Assumption 4 extend those of Blasques et al (2014b) by allowing for exogenous regressors.…”

Modeling Financial Sector Joint Tail Risk in the Euro Area

“…Deriving the asymptotic behavior for time varying parameter models with GAS dynamics is non-trivial. We refer to Blasques et al (2012Blasques et al ( , 2014 for details.…”