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In this article, we study a family of so-called semi-strong augmented GARCH(1,1) model where the innovation process is strictly stationary and mixing instead of independent and identically distributed. We give a necessary and sufficient condition for stationarity of the process and study the functional central limit theorems forand  u twhen the process is stationary. We also investigate the dynamic behavior of semi-strong GARCH(1,1) model when it is non stationary.

Asymptotics for semi-strong augmented GARCH(1,1) model