STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM
STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM
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DOI：
10.1017/s0266466600161018
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发表时间：
2000-02
影响因子：
0.8
通讯作者：
L. Giraitis;P. Kokoszka;R. Leipus
中科院分区：
文献类型：
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作者：
L. Giraitis;P. Kokoszka;R. Leipus
本文研究了一类广泛的非负∞模型。建立了平稳解存在的充分条件，并得到了该解的沃尔泰拉型级数的显式表示，在我们的假设下，协方差函数可以像幂函数一样缓慢衰减，刚好达到长记忆结构.建立了鞅差的移动平均表示，证明了中心极限定理。
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.