AGGREGATION OF THE RANDOM COEFFICIENT GLARCH(1,1) PROCESS
研究了线性ARCH模型（LARCH）的同期聚合，证明当系数服从Beta分布时，聚合后的广义LARCH(1,1)过程具有长记忆性，其平方的相关性缓慢衰减，部分和收敛到一种新型自相似过程。
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.