Inconsistency for the Gaussian QMLE in GARCH-type models with infinite variance

Stelios Arvanitis and Alexandros Louka

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 5, 1684-1699

Abstract: We are occupied with the issue of consistency of the Gaussian QMLE in GARCH-type models with very heavy tailed squared innovations. We show that the appropriately scaled likelihood function weakly epi-converges to a stochastic process that is a.s. lower semi-continuous and proper. When moreover the volatility filter is increasing w.r.t. the parameter, inconsistency follows due to that the true parameter value misses the set of minimizers of the limit. This holds for models like the AGARCH, the Augmented GARCH, and the GQARCH.

Date: 2024
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DOI: 10.1080/03610926.2022.2107665

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