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随机系数 GLARCH(1,1) 过程的同期聚合AI 解读

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…

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ARCH(∞) 模型的平稳性AI 解读

We continue investigation of the ARCH(∞) model begun in Giraitis, Kokoszka, and Leipus (2000, Econometric Theory 16, 3–22). Nonrestrictive conditions for the existence of a strictly stationary solution are established. The paper generalizes the results of Nelson (1990, Econometric Theory 6, 318–334) and Bougerol and Picard (1992, Journal of Econometrics 52, 115–127) to the ARCH(∞) model.

平稳 ARCH 模型：依赖结构与中心极限定理AI 解读

This paper studies a broad class of nonnegative ARCH(∞) models. Sufficient conditions for the existence of a stationary solution are established and an explicit representation of the solution as a Volterra type series is found. Under our assumptions, the covariance function can decay slowly like a power function, falling just short of the long memory structure. A moving average representation in martingale differences is established, and the central limit theorem is proved.