MIXING PROPERTIES OF A GENERAL CLASS OF GARCH(1,1) MODELS WITHOUT MOMENT ASSUMPTIONS ON THE OBSERVED PROCESS
MIXING PROPERTIES OF A GENERAL CLASS OF GARCH(1,1) MODELS WITHOUT MOMENT ASSUMPTIONS ON THE OBSERVED PROCESS
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DOI：
10.1017/s0266466606060373
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发表时间：
2006-08
影响因子：
0.8
通讯作者：
C. Francq;Jean-Michel Zakoïan
中科院分区：
文献类型：
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作者：
C. Francq;Jean-Michel Zakoïan
我们考虑一般的，可能是非参数的，Gestival（1，1）过程。首先给出了平稳遍历解存在唯一的条件。然后，我们确定几何遍历的附加条件。这些条件包括对潜在独立过程的分布的温和限制。对广义自回归条件异方差（GARCH）过程不作矩假设.提出了样本自相关的渐近行为和单位根检验的应用。这项工作得到了INTAS的支持（研究项目03-51-3714）。作者感谢布鲁斯汉森和三位审稿人对手稿的快速和仔细的阅读。他们的详细评论使报告的格式大为改进。
We consider general, and possibly nonparametric, GARCH(1,1) processes. First we give conditions for the existence and the uniqueness of stationary ergodic solutions. Then we identify additional conditions for geometric ergodicity. These conditions consist of mild restrictions on the distribution of the latent independent process. No moment assumption is made on the generalized autoregressive conditionally heteroskedastic (GARCH) process. Applications to the asymptotic behavior of sample autocorrelations and to unit-root tests are proposed.This work was supported by INTAS (research project 03-51-3714). The authors gratefully acknowledge the quick and careful reading of the manuscript by Bruce Hansen and three referees. Their detailed comments led to a greatly improved presentation.