STATIONARITY AND MEMORY OF ARCH([infty infinity]) MODELS

Paolo Zaffaroni

Econometric Theory, 2004, vol. 20, issue 01, pages 147-160

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.

Date: 2004

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Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:20:y:2004:i:01:p:147-160_20

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