Although the properties of the ARCH(∞) model are well investigated, the existence of long memory FIGARCH and IARCH solution was not established in the literature. These two popular ARCH type models which are widely used in applied literature, were causing theoretical controversy because of the...

We discuss joint temporal and contemporaneous aggregation of N independent copies of AR(1) process with random-coefficient a∈[0,1) when N and time scale n increase at different rate. Assuming that a has a density, regularly varying at a=1 with exponent −1β1, different joint limits of...

Although the properties of the ARCH(∞) model are well investigated, the existence of long memory FIGARCH and IARCH solution was not established in the literature. These two popular ARCH type models which are widely used in applied literature, were causing theoretical controversy because of the...