MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Semi parametric estimation of extremal index for ARMAX process with infinite variance
Hakim Ouadjed and Mami Tawfiq Fawzi

Abstract

We consider estimating the extremal index of a maximum autoregressive process of order one under the assumption that the distribution of the innovations has a regularly varying tail at infinity. We establish the asymptotic normality of the new estimator using the extreme quantile approach, and its performance is illustrated in a simulation study. Moreover, we compare, in terms of bias and mean squared error, our estimator with the estimator of Ferro and Segers [Inference for clusters of extreme values, J. Royal Stat. Soc., Ser. B, {65} (2003), 545--556] and Olmo [A new family of consistent and asymptotically-normal estimators for the extremal index, {Econometrics}, 3 (2015), 633--653].

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Keywords: extreme value theory; max autoregressive processes; tail index estimation

MSC: 60G70, 62G32

Pages:  130--139     

Volume  68 ,  Issue  2 ,  2016