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INFERENCE ON GARCH-MIDAS MODELS WITHOUT ANY SMALL-ORDER MOMENT

Published online by Cambridge University Press:  12 May 2023

Christian Francq Open the ORCID record for Christian Francq [Opens in a new window] ,
Baye Matar Kandji Open the ORCID record for Baye Matar Kandji [Opens in a new window]  and
Jean-Michel Zakoian Open the ORCID record for Jean-Michel Zakoian [Opens in a new window]
Christian Francq
Affiliation:
CREST–ENSAE and University of Lille
Baye Matar Kandji
Affiliation:
CREST–ENSAE
Jean-Michel Zakoian*
Affiliation:
CREST-ENSAE and University of Lille
*
Address correspondence to Jean-Michel Zakoïan, CREST–ENSAE, Palaiseau, France; e-mail: zakoian@ensae.fr
Rights & Permissions [Opens in a new window]

Abstract

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In GARCH-mixed-data sampling models, the volatility is decomposed into the product of two factors which are often interpreted as “short-run” (high-frequency) and “long-run” (low-frequency) components. While two-component volatility models are widely used in applied works, some of their theoretical properties remain unexplored. We show that the strictly stationary solutions of such models do not admit any small-order finite moment, contrary to classical GARCH. It is shown that the strong consistency and the asymptotic normality of the quasi-maximum likelihood estimator hold despite the absence of moments. Tests for the presence of a long-run volatility relying on the asymptotic theory and a bootstrap procedure are proposed. Our results are illustrated via Monte Carlo experiments and real financial data.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 34
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Footnotes

The authors are grateful to two anonymous referees, the Co-Editor, and the Editor for insightful comments, suggestions, and useful criticisms. The authors are also grateful to the Agence Nationale de la Recherche (ANR), which supported this work via the Project MLforRisk (ANR-21-CE26-0007).

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