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2017 Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models
Randal Douc, Konstantinos Fokianos, Eric Moulines
Electron. J. Statist. 11(2): 2707-2740 (2017). DOI: 10.1214/17-EJS1299


We study a general class of quasi-maximum likelihood estimators for observation-driven time series models. Our main focus is on models related to the exponential family of distributions like Poisson based models for count time series or duration models. However, the proposed approach is more general and covers a variety of time series models including the ordinary GARCH model which has been studied extensively in the literature. We provide general conditions under which quasi-maximum likelihood estimators can be analyzed for this class of time series models and we prove that these estimators are consistent and asymptotically normally distributed regardless of the true data generating process. We illustrate our results using classical examples of quasi-maximum likelihood estimation including standard GARCH models, duration models, Poisson type autoregressions and ARMA models with GARCH errors. Our contribution unifies the existing theory and gives conditions for proving consistency and asymptotic normality in a variety of situations.


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Randal Douc. Konstantinos Fokianos. Eric Moulines. "Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models." Electron. J. Statist. 11 (2) 2707 - 2740, 2017.


Received: 1 April 2016; Published: 2017
First available in Project Euclid: 4 July 2017

zbMATH: 1366.62173
MathSciNet: MR3679907
Digital Object Identifier: 10.1214/17-EJS1299

Primary: 60J05 , 62M10
Secondary: 62M05

Keywords: asymptotic normality , consistency , Count time series , duration models , GARCH models , Kullback-Leibler divergence , maximum likelihood , stationarity


Vol.11 • No. 2 • 2017
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