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 for (Formula presented.) and ut when the process is stationary. We also investigate the dynamic behavior of semi-strong GARCH(1,1) model when it is non stationary.
- functional central limit theorem
- L -NED
- Semi-strong augmented GARCH(1,1) model