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. Abstract Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised. We derive considerably weaker conditions that can be used in practice to ensure the consistency of the maximum likelihood estimator for a wide class of observation-driven time series models. Our consistency results hold for both correctly specified and misspecified models. The practical relevance of the theory is highlighted in a set of empirical examples. We further obtain an asymptotic test and confidence bounds for the unfeasible "true" invertibility region of the parameter space. Terms of use: Documents in

Summary The paper introduces a general class of heavy-tailed auto-regressions for modelling integer-valued time series with outliers. The specification proposed is based on a heavy-tailed mixture of negative binomial distributions that features an observation-driven dynamic equation for the conditional expectation. The existence of a stationary and ergodic solution for the class of auto-regressive processes is shown under general conditions. The estimation of the model can be easily performed by maximum likelihood given the closed form of the likelihood function. The strong consistency and the asymptotic normality of the estimator are formally derived. Two examples of specifications illustrate the flexibility of the approach and the relevance of the theoretical results. In particular, a linear dynamic equation and a score-driven equation for the conditional expectation are studied. The score-driven specification is shown to be particularly appealing as it delivers a robust filtering method that attenuates the effect of outliers. Empirical applications to the series of narcotics trafficking reports in Sydney and the euro–pound sterling exchange rate illustrate the effectiveness of the method in handling extreme observations.

We propose a novel multivariate GARCH model that incorporates realized measures for the variance matrix of returns. The key novelty is the joint formulation of a multivariate dynamic model for outer-products of returns, realized variances and realized covariances. The updating of the variance matrix relies on the score function of the joint likelihood function based on Gaussian and Wishart densities. The dynamic model is parsimonious while each innovation still impacts all elements of the variance matrix. Monte Carlo evidence for parameter estimation based on different small sample sizes is provided. We illustrate the model with an empirical application to a portfolio of 15 U.S. financial assets.

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