EMPIRICAL LIKELIHOOD FOR GARCH MODELS
EMPIRICAL LIKELIHOOD FOR GARCH MODELS
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DOI：
10.1017/s0266466606060208
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发表时间：
2006-03
影响因子：
0.8
通讯作者：
N. Chan;S. Ling
中科院分区：
文献类型：
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作者：
N. Chan;S. Ling
本文对正则广义自回归条件异方差（GARCH）模型和具有单位根的GARCH模型提出了一种经验似然方法。对于正则Gestival模型，证明了对数经验似然比统计量渐近服从χ 2分布.对于具有单位根的Gestival模型，考虑了经验似然方法的两个版本，最小二乘得分和最大似然得分函数。对于这两种情况，对数经验似然比统计量的极限分布的建立。这两个统计量可用于在Gynecological框架下测试单位根。本研究获香港研究资助局赠款CUHK 4043/02 P及HKUST 6273/03 H部分资助。作者感谢两位评审和共同编辑布鲁斯汉森，他们对QMLE和MELE之间的关系提出了有见地和有帮助的评论，这导致了演示文稿的实质性改进。Jerry Wong和Chun-Yip Yau的计算帮助也得到了感谢。
This paper develops an empirical likelihood approach for regular generalized autoregressive conditional heteroskedasticity (GARCH) models and GARCH models with unit roots. For regular GARCH models, it is shown that the log empirical likelihood ratio statistic asymptotically follows a χ2 distribution. For GARCH models with unit roots, two versions of the empirical likelihood methods, the least squares score and the maximum likelihood score functions, are considered. For both cases, the limiting distributions of the log empirical likelihood ratio statistics are established. These two statistics can be used to test for unit roots under the GARCH framework. Finite-sample performances are assessed through simulations for GARCH models with unit roots.This research was supported in part by Hong Kong Research grants Council Grants CUHK4043/02P and HKUST6273/03H. The authors thank two referees and the Co-Editor, Bruce Hansen, for insightful and helpful comments about the relationship between QMLE and MELE, which led to substantial improvement of the presentation. Computational assistance from Jerry Wong and Chun-Yip Yau is also gratefully acknowledged.