Stationarity and Memory of ARCH Models
AbstractSufficient 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.
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Bibliographic InfoPaper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2000/383.
Date of creation: Mar 2000
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ARCH(8); GARCH(p; q); nonlinear moving average representation; strict and weak stationarity; memory.;
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