Abstract :
The paper discusses contemporaneous aggregation of the Linear ARCH (LARCH)
model as defined in (1), which was introduced in Robinson (1991) and studied in
Giraitis, Robinson, and Surgailis (2000) and other works. We show that the limiting
aggregate of the (G)eneralized LARCH(1,1) process in (3)–(4) with random Beta
distributed coefficient β exhibits long memory. In particular, we prove that squares
of the limiting aggregated process have slowly decaying correlations and their partial
sums converge to a self-similar process of a new type.
