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STATIONARITY AND MEMORY OF ARCH(∞) MODELS

Published online by Cambridge University Press:  05 March 2004

Paolo Zaffaroni
Paolo Zaffaroni
Affiliation:
Banca d'Italia
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Abstract

We establish the necessary and sufficient conditions for covariance stationarity of ARCH(∞), for both the levels and the squares. The result applies to any form of the conditional variance coefficients. This includes GARCH(p,q) and also specifications with hyperbolically decaying coefficients, such as the autoregressive coefficients of the autoregressive fractionally integrated moving average model. The covariance stationarity condition for the levels rules out long memory in the squares.I thank Peter M. Robinson for useful comments on previous versions of the paper. Also, I am grateful to the co-editor (Bruce E. Hansen) and an anonymous referee whose suggestions greatly improved the paper.

Type
Research Article
Information
Econometric Theory , Volume 20 , Issue 1 , February 2004 , pp. 147 - 160
Copyright
© 2004 Cambridge University Press

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