test_moissonnage_selune
type: Agent

Continuous invertibility and stable QML estimation of the EGARCH(1,1) model
type: Distribution
access URL: https://hal.science/hal-00751706
format: HTML
issued: 2026-05-15T13:25:18.112155
modified: 2026-05-15T13:25:18.070859

Continuous invertibility and stable QML estimation of the EGARCH(1,1) model
type: Dataset
contact point: Organization
  fn: CCSD
keyword: invertible-models
keyword: asymptotic-normality
keyword: infoeu-reposemanticsarticle
keyword: strong-consistency
keyword: quasi-maximum-likelihood
keyword: journal-articles
keyword: volatility-models
keyword: primary-62f12-secondary-60h25-62f10-62m20-62m10-91b84
keyword: statthstatistics-statstatistics-theory-statth
keyword: stochastic-recurrence-equation
keyword: exponential-garch
keyword: mathmath-stmathematics-mathstatistics-mathst
landing page: 0303-6898
description: We introduce the notion of continuous invertibility on a compact set for volatility models driven by a Stochastic Recurrence Equation (SRE). We prove the strong consistency of the Quasi Maximum Likelihood Estimator (QMLE) when the optimization procedure is done on a continuously invertible domain. This approach gives for the first time the strong consistency of the QMLE used by Nelson in \cite{nelson:1991} for the EGARCH(1,1) model under explicit but non observable conditions. In practice, we propose to stabilize the QMLE by constraining the optimization procedure to an empirical continuously invertible domain. The new method, called Stable QMLE (SQMLE), is strongly consistent when the observations follow an invertible EGARCH(1,1) model. We also give the asymptotic normality of the SQMLE under additional minimal assumptions.
issued: 2026-05-15T13:25:18.104236
language: en
modified: 2026-05-15T13:25:18.104242