Following the original paper of Nelson (Econometrica, 91), if you define
the EGARCH as
ln[h(t)] = alpha(t) + SUM(k=1,infinite) [ beta(k) g(z(t-k)) ]
with g[z(t)] = theta z(t) + gamma [|z(t)| - E|z(t)|],
Theorem 2.1 (p.354) gives the condition for the covariance stationarity of
{ln[h(t)] - alpha(t)}, i.e. SUM(k=1, infinite) beta(k)^2 < infinite. (see
the original paper for more details).
Regards,
Jean-Philippe Peters
University of Liege,
Belgium.
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A 03:53 PM 7/30/01 -0600, David Leblang a écrit :
>HI:
>
>In the standard GARCH (1,1) model, it is said that the garch process
>contains a unit root if A (the parameter estimate on the ARCH term) + B
>(the parameter estimate on the GARCH term) equal 1.
>
>However, in the EGARCH setup, there are three parameters: A, B and E, where
>E captures the asymmetric component of the arch process.
>
>In EGARCH, then, how do you evaluate stationarity?
>
>Thanks,
>
>David Leblang
>University of Colorado
>
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