Maximum Likelihood Estimation for correctly Specified Generalized Autoregressive Score Models: Feedback Effects, Contraction Conditions and Asymptotic Properties

Francisco Blasques (), Siem Jan Koopman and Andre Lucas

No 14-074/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: The 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.

Keywords: Observation-driven models; stochastic recurrence equations; contraction conditions; invertibility; stationarity; ergodicity; generalized autoregressive score models (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 (search for similar items in EconPapers)
Date: 2014-06-20
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (9)

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