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A NECESSARY AND SUFFICIENT CONDITION FOR THE STRICT STATIONARITY OF A FAMILY OF GARCH PROCESSES

Published online by Cambridge University Press:  30 August 2006

Mika Meitz
Mika Meitz
Affiliation:
Stockholm School of Economics
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Abstract

We consider a family of GARCH(1,1) processes introduced in He and Teräsvirta (1999a, Journal of Econometrics 92, 173–192). This family contains various popular generalized autoregressive conditional heteroskedasticity (GARCH) models as special cases. A necessary and sufficient condition for the existence of a strictly stationary solution is given.This research was financially supported by the Jan Wallander's and Tom Hedelius' Foundation, Grant J03–41. The author thanks the editor, an anonymous referee, Pentti Saikkonen, and Timo Teräsvirta for useful comments.

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 22 , Issue 5 , October 2006 , pp. 985 - 988
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307–327.Google Scholar
Bougerol, P. & N. Picard (1992) Stationarity of GARCH processes and some nonnegative time series. Journal of Econometrics 52, 115–127.Google Scholar
Duan, J.-C. (1997) Augmented GARCH(p,q) process and its diffusion limit. Journal of Econometrics 79, 97–127.Google Scholar
Glosten, L.W., R. Jaganathan, & D.E. Runkle (1993) On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance 48, 1779–1801.Google Scholar
He, C. & T. Teräsvirta (1999a) Properties of moments of a family of GARCH processes. Journal of Econometrics 92, 173–192.Google Scholar
He, C. & T. Teräsvirta (1999b) Statistical properties of the asymmetric power ARCH process. In R.F. Engle & H. White (eds.), Cointegration, Causality, and Forecasting: A Festschrift in Honour of Clive W. J. Granger, pp. 462–474. Oxford University Press.
Ling, S. & M. McAleer (2002) Stationarity and the existence of moments of a family of GARCH processes. Journal of Econometrics 106, 109–117.Google Scholar
Nelson, D. (1990) Stationarity and persistence in the GARCH(1,1) model. Econometric Theory 6, 318–334.Google Scholar
Schwert, G.W. (1989) Why does stock market volatility change over time? Journal of Finance 44, 1115–1153.Google Scholar
Taylor, S. (1986) Modelling Financial Time Series. Wiley.