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Title: Inference on multiplicative component GARCH without any small-order moment Authors:  Baye Matar Kandji - CREST/Institut Polytechnique de Paris (France) [presenting]
Christian Francq - CREST and University Lille III (France)
Jean-Michel Zakoian - CREST (France)
Abstract: In multiplicative component GARCH models, the volatility is decomposed into the product of two factors which often receive 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 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 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.