Arbeitspapier
Non-negativity conditions for the hyperbolic GARCH model
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(1) 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.
- Sprache
-
Englisch
- Erschienen in
-
Series: KOF Working Papers ; No. 162
- Klassifikation
-
Wirtschaft
Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
Model Evaluation, Validation, and Selection
Forecasting Models; Simulation Methods
- Thema
-
Inequality constraints
fractional integration
long memory GARCH processes
ARCH-Modell
Modell-Spezifikation
Zeitreihenanalyse
Theorie
- Ereignis
-
Geistige Schöpfung
- (wer)
-
Conrad, Christian
- Ereignis
-
Veröffentlichung
- (wer)
-
ETH Zurich, KOF Swiss Economic Institute
- (wo)
-
Zurich
- (wann)
-
2007
- DOI
-
doi:10.3929/ethz-a-005390226
- Handle
- Letzte Aktualisierung
-
10.03.2025, 11:41 MEZ
Datenpartner
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Objekttyp
- Arbeitspapier
Beteiligte
- Conrad, Christian
- ETH Zurich, KOF Swiss Economic Institute
Entstanden
- 2007
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