 On IGARCH and convergence of the QMLE for misspecified GARCH modelsAnders Tolver Jensen () and
Theis Lange
CREATES Research Papers from Department of Economics and Business Economics, Aarhus University Abstract: We address the IGARCH puzzle by which we understand the fact that a GARCH(1,1) model fitted by quasi maximum likelihood estimation to virtually any financial dataset exhibit the property that alpha^hat + beta^hat is close to one. We prove that if data is generated by certain types of continuous time stochastic volatility models, but fitted to a GARCH(1,1) model one gets that alpha^hat + beta^hat tends to one in probability as the sampling frequency is increased. Hence, the paper suggests that the IGARCH effect could be caused by misspecification. The result establishes that the stochastic sequence of QMLEs do indeed behave as the deterministic parameters considered in the literature on filtering based on misspecified ARCH models, see e.g. Nelson (1992). An included study of simulations and empirical high frequency data is found to be in very good accordance with the mathematical results. Keywords: GARCH; Integrated GARCH; Misspecification; High frequency exchange rates (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2009-06 Access Statistics for this paper More papers in CREATES Research Papers from Department of Economics and Business Economics, Aarhus University |
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