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On the limit theory of the Gaussian SQMLE in the EGARCH(1,1) model
Author(s) -
Arvanitis Stelios,
Anyfantaki Sofia
Publication year - 2020
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12494
Subject(s) - mathematics , estimator , limit (mathematics) , gaussian , asymptotic analysis , limiting , gaussian process , monte carlo method , asymptotic distribution , parameter space , statistical physics , statistics , mathematical analysis , mechanical engineering , physics , quantum mechanics , engineering
We derive the limit theory of the Gaussian stable quasi maximum likelihood estimator for the stationary EGARCH(1,1) model when the squared innovation process has marginals with regularly varying tails. We derive regularly varying rates and limiting stable distributions. We perform Monte Carlo experiments to assess the extent of the parameter space corresponding to the invertibility condition, and the quality of the asymptotic approximation.