
Open access
Author
Date
2007-04Type
- Working Paper
ETH Bibliography
yes
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Abstract
In this article we derive conditions which ensure the non-negativity of the conditional variance in the Hyperbolic GARCH(p,d,q) (HYGARCH) model of Davidson (2004). The conditions are necessary and sufficient for p ≤ 2 and sufficient for p > 2 and emerge as natural extensions of the inequality constraints derived in Nelson and Cao (1992) for the GARCH model and in Conrad and Haag (2006) for the FIGARCH model. As a by-product we obtain a representation of the ARCH(∞) coefficients which allows computationally efficient multi-step-ahead forecasting of the conditional variance of a HYGARCH process. We also relate the necessary and sufficient parameter set of the HYGARCH to the necessary and sufficient parameter sets of its GARCH and FIGARCH components. Finally, we analyze the effects of erroneously fitting a FIGARCH model to a data sample which was truly generated by a HYGARCH process. An empirical application of the HYGARCH(1,d,1) model to daily NYSE data illustrates the importance of our results. Show more
Permanent link
https://doi.org/10.3929/ethz-a-005390226Publication status
publishedJournal / series
KOF Working PapersVolume
Publisher
KOF Swiss Economic Institute, ETH ZurichSubject
MODELS + MATHEMATICAL MODELING (SOCIAL SCIENCES); Long memory GARCH processes; Fractional integration; MODELLE + MODELLRECHNUNG (SOZIALWISSENSCHFTEN); Inequality constraintsOrganisational unit
02525 - KOF Konjunkturforschungsstelle / KOF Swiss Economic Institute
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ETH Bibliography
yes
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