Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model

By Olivier Wintenberger. 2012

87 citations recorded by the source corpus.

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.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/162d23b0ea5c5c469aa7e26c6f9b185761b8412a

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Citations in the corpus

QML INFERENCE FOR VOLATILITY MODELS WITH COVARIATES (2015, unknown): “The inference of the EGARCH is however quite difficult, and the behaviour of the QMLE is still partially unknown for this model (see Wintenberger, 2013).”
Feasible invertibility conditions and maximum likelihood estimation for observation-driven models (2018, methodology): “In this regard, [47] introduces the notion of continuous invertibility for GARCH-type models to ensure the uniform convergence of the filtered volatility.”
Risk-parameter estimation in volatility models (2012, background): “See Sucarrat and Escribano (2010), Wintenberger (2013) for recent references on the log-GARCH and EGARCH, and Francq and Zakoïan (2010) for references on the other specifications.”
Spillover Dynamics for Systemic Risk Measurement Using Spatial Financial Time Series Models (2016, unknown): “Invertibility is a key property for establishing consistency and asymptotic normality of the MLE; see for example Wintenberger (2013).”
GARCH models without positivity constraints: Exponential or log GARCH? (2012, methodology): “As in Section 5 of Bardet and Wintenberger (2009), the asymptotic normality is obtained by showing: 1.”
Maximum Likelihood Estimation for Generalized Autoregressive Score Models (2014, unknown): “…well as e.a.s. convergence of the filtered parameter {f̃t(θ, f̄1)}t∈N to a strictly stationary and ergodic (SE) limit process {f̃t(θ)}t∈Z with E log+ |φy(f, yt;θ)| <∞, E log sup f |φ′y(f, yt;θ)| < 0, where φ′y(f, yt;θ) := ∂φy(f, yt;θ)/∂f ; see Straumann and Mikosch (2006) and Wintenberger (2013).”
A One Line Derivation of EGARCH (2014, background): “Wintenberger [13] proves consistency using continuous invertibility, which is assumed to hold for the EGARCH(1,1) model, and shows asymptotic normality for the quasi-maximum likelihood estimator of EGARCH(1,1) under “non-verifiable” conditions, and asymptotic normality for the stable quasi-maximum l”