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Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model
Author(s) -
Wintenberger Olivier
Publication year - 2013
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12038
Subject(s) - mathematics , invertible matrix , strong consistency , estimator , heteroscedasticity , asymptotic distribution , autoregressive model , volatility (finance) , consistency (knowledge bases) , exponential function , autoregressive conditional heteroskedasticity , econometrics , statistics , mathematical analysis , pure mathematics , discrete mathematics
I introduce the notion of continuous invertibility on a compact set for volatility models driven by a stochastic recurrence equation. I prove strong consistency of the quasi‐maximum likelihood estimator (QMLE) when the quasi‐likelihood criterion is maximized on a continuously invertible domain. This approach yields, for the first time, the asymptotic normality of the QMLE for the exponential general autoregressive conditional heteroskedastic (EGARCH(1,1)) model under explicit but non‐verifiable conditions. In practice, I propose to stabilize the QMLE by constraining the optimization procedure to an empirical continuously invertible domain. The new method, called stable QMLE, is asymptotically normal when the observations follow an invertible EGARCH(1,1) model.