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Non-negativity Conditions for the Hyperbolic GARCH Model

Christian Conrad

No 07-162, KOF Working papers from KOF Swiss Economic Institute, ETH Zurich

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 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.

Keywords: Inequality constraints; Fractional integration; Long memory GARCH processes (search for similar items in EconPapers)
Pages: 24 pages
Date: 2007-04
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-for
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Citations: View citations in EconPapers (8)

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Journal Article: Non-negativity conditions for the hyperbolic GARCH model (2010) Downloads
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