Stationarity and Memory of ARCH Models

Paolo Zaffaroni

STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE

Abstract: Sufficient conditions for strict stationarity of ARCH(8) are established, without imposing covariance stationarity and for any specification of the conditional second moment coefficients. GARCH(p,q) as well as the case of hyperbolically decaying coefficients are included, such as the autoregressive coefficients of ARFIMA(p,d,q), once the non-negativity constraints are imposed. Second, we show the necessary and sufficient conditions for covariance stationarity of ARCH(8), both for the levels and the squares. These prove to be much stronger than the strict stationarity conditions. The covariance stationarity condition for the levels rules out long memory in the squares.

Keywords: ARCH(8); GARCH(p; q); nonlinear moving average representation; strict and weak stationarity; memory. (search for similar items in EconPapers)
Date: 2000-03
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Citations: View citations in EconPapers (3)

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Related works:
Working Paper: Stationarity and memory of ARCH models (2000)
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Persistent link: https://EconPapers.repec.org/RePEc:cep:stiecm:383

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