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A NOTE ON INEQUALITY CONSTRAINTS IN THE GARCH MODEL

Published online by Cambridge University Press:  26 February 2008

Henghsiu Tsai  and
Kung-Sik Chan
Henghsiu Tsai*
Affiliation:
Academia Sinica
Kung-Sik Chan
Affiliation:
University of Iowa
*
Address correspondence to Henghsiu Tsai, Institute of Statistical Science, Academia Sinica, 128, Academia Rd. Sec. 2, Taipei 115, Taiwan; e-mail: htsai@stat.sinica.edu.tw.
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Abstract

We consider the parameter restrictions that need to be imposed to ensure that the conditional variance process of a GARCH(p,q) model remains nonnegative. Previously, Nelson and Cao (1992, Journal of Business ’ Economic Statistics 10, 229–235) provided a set of necessary and sufficient conditions for the aforementioned nonnegativity property for GARCH(p,q) models with p ≤ 2 and derived a sufficient condition for the general case of GARCH(p,q) models with p ≥ 3. In this paper, we show that the sufficient condition of Nelson and Cao (1992) for p ≥ 3 actually is also a necessary condition. In addition, we point out the linkage between the absolute monotonicity of the generalized autoregressive conditional heteroskedastic (GARCH) generating function and the nonnegativity of the GARCH kernel, and we use it to provide examples of sufficient conditions for this nonnegativity property to hold.

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 24 , Issue 3 , June 2008 , pp. 823 - 828
Copyright
Copyright © Cambridge University Press 2008

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References

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