Inference on Multiplicative Component GARCH without any Small-Order Moment

Christian Francq, Baye Matar Kandji () and Jean-Michel Zakoian
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Baye Matar Kandji: CREST-ENSAE

No 2022-09, Working Papers from Center for Research in Economics and Statistics

Abstract: In multiplicative component GARCH models, the volatility is decomposed into the product of two factors which often received interpretations in terms of "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 nite 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 nancial data.

Keywords: GARCH-MIDAS; Moments existence; QMLE; Residual Bootstrap; Tests on boundary parameters. (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 C58 (search for similar items in EconPapers)
Pages: 37 pages
Date: 2022-03-18
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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