Stationarity and functional central limit theorem for ARCH(∞) models

In this paper, we study the stationarity and functional central limit theorem for (random coefficient) ARCH(∞) models including HYAPGARCH and mixture memory GARCH models. Those models are able to cover long memory property with fewer parameters and have finite variances. The functional central limit theorems for ut and the squared processes ut2 and σt2 are proved. Sufficient conditions for L2-NED property to hold are established and the FCLT for mixture memory GARCH model as an example of a random coefficient ARCH(∞) process is derived via L2-NED condition.