Resource title

Stationarity and memory of ARCH models

Resource image

image for OpenScout resource :: Stationarity and memory of ARCH models

Resource description

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.

Resource author

Resource publisher

Resource publish date

Resource language


Resource content type


Resource resource URL

Resource license