GARCH模型两步厚尾估计的诊断检验

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GARCH模型两步厚尾估计的诊断检验冯牧¹, 王萌², 龚朝庭³1. 中国科学技术大学统计与金融系, 合肥 230026;
2. 博时基金管理有限公司, 深圳 518000;
3. 中国科学院数学与系统科学研究院, 北京 100190 Diagnostic Test for the Two-step Estimators of Heavy-tailed GARCH Models FENG Mu¹, WANG Meng², GONG Chaoting³1. University of Science and Technology of China, Hefei 230026, China;
2. Boshi Fund Management Co., LTD, Shenzhen 518000, China;
3. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China

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摘要GARCH模型在金融时间序列建模中有广泛的应用，其参数的估计精度和模型的诊断检验一直是人们关注的两大问题.本文针对平稳GARCH模型，构建了新的两步NGQMELE，在残差的二阶矩有限情况下建立了两步NGQMELE的相合性和渐进正态性.另外，针对该估计提出了基于残差绝对值及平方值的自相关函数的拟合优度检验统计量Q（M），Q²（M），并分别在二阶矩有限和四阶矩有限的情况下证明了它们的渐进性质.数值模拟和实例分析结果都显示出Q（M）是在厚尾情形下更优的一个检验.

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收稿日期: 2016-11-30

PACS:

O212.1

基金资助:国家自然科学基金（11671102，11361011）和广西自然科学基金（2016GXNSFAA3800163）资助项目.

引用本文:

冯牧, 王萌, 龚朝庭. GARCH模型两步厚尾估计的诊断检验[J]. 应用数学学报, 2018, 41(1): 55-70. FENG Mu, WANG Meng, GONG Chaoting. Diagnostic Test for the Two-step Estimators of Heavy-tailed GARCH Models. Acta Mathematicae Applicatae Sinica, 2018, 41(1): 55-70.

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