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Non-negativity Conditions for the Hyperbolic GARCH Model

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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 suffcient 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(1) coeffcients which allows computationally effcient multi-step-ahead forecasting of the conditional variance of a HYGARCH process. We also relate the necessary and suffcient parameter set of the HYGARCH to the necessary and su±cient 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.

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Paper provided by KOF Swiss Economic Institute, ETH Zurich in its series KOF Working papers with number 07-162.

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Length: 26 pages
Date of creation: Apr 2007
Date of revision:
Handle: RePEc:kof:wpskof:07-162

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Keywords: Inequality constraints; fractional integration; long memory GARCH processes;

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Cited by:
  1. Rafik Nazarian & Esmaeil Naderi & Nadiya G. Alikhani & Ashkan Amiri, 2014. "Long Memory Analysis: An Empirical Investigation," International Journal of Economics and Financial Issues, Econjournals, vol. 4(1), pages 16-26.
  2. Conrad, Christian & Loch, Karin & Rittler, Daniel, 2012. "On the Macroeconomic Determinants of the Long-Term Oil-Stock Correlation," Working Papers 0525, University of Heidelberg, Department of Economics.
  3. Christian Conrad & Menelaos Karanasos, 2008. "Negative Volatility Spillovers in the Unrestricted ECCC-GARCH Model," KOF Working papers 08-189, KOF Swiss Economic Institute, ETH Zurich.
  4. Charles, Amélie & Darné, Olivier, 2014. "Volatility persistence in crude oil markets," Energy Policy, Elsevier, vol. 65(C), pages 729-742.
  5. Conrad, Christian & Loch, Karin, 2012. "Anticipating Long-Term Stock Market Volatility," Working Papers 0535, University of Heidelberg, Department of Economics.
  6. Mohamed Chikhi & Anne Peguin-Feissolle & Michel Terraza, 2012. "SEMIFARMA-HYGARCH Modeling of Dow Jones Return Persistence," Working Papers halshs-00793203, HAL.
  7. Christian Conrad & Menelaos Karanasos & Ning Zeng, 2008. "Multivariate Fractionally Integrated APARCH Modeling of Stock Market Volatility: A multi-country study," Working Papers 0472, University of Heidelberg, Department of Economics, revised Jul 2008.
  8. Conrad, Christian & Rittler, Daniel & Rotfuß, Waldemar, 2010. "Modeling and Explaining the Dynamics of European Union Allowance Prices at High-Frequency," Working Papers 0497, University of Heidelberg, Department of Economics.
  9. repec:wyi:journl:002190 is not listed on IDEAS

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