统计研究 ›› 2018, Vol. 35 ›› Issue (5): 119-128.doi: 10.19343/j.cnki.11-1302/c.2018.05.012

• • 上一篇    

非线性GARCH族的模型平均估计方法

姚青松等   

  • 出版日期:2018-05-25 发布日期:2018-05-25

Model Averaging Estimation Method for Nonlinear GARCH Family

Yao Qingsong et al.   

  • Online:2018-05-25 Published:2018-05-25

摘要: 本文考虑了非线性GARCH族的模型平均估计方法。在备选模型集合包含拥有不同模型结构的非线性GARCH族的情况下,本文构建了非线性GARCH族的模型平均估计量,并给出相应的权重选择准则。在一定正则条件下,本文证明上述模型平均估计量具有渐近最优性,即渐近实现真实最优的KL偏离度。蒙特卡洛模拟结果表明,在大部分情形下,本文提出的模型平均估计量取得了更小的相对KL偏离值。作为非线性GARCH族的模型平均估计方法的应用,本文对2016年6月1日至2017年6月1日上证指数的日波动率进行估计,与现有模型选择与模型平均方法相比较,本文模型平均估计方法具有更高的精度。

关键词: 模型平均, 非线性GARCH族, 渐近最优性, 已实现波动率

Abstract: This paper uses the model averaging estimation for nonlinear GARCH family. As the optional model set contains nonlinear GARCH families with different functional forms, this paper constructs model averaging estimators with the nonlinear GARCH family, and presents a criterion for choosing the corresponding weights. Under certain canonical conditions, this paper proves the optimality of the above-mentioned model averaging estimators, i.e., asymptotically achieving the minimum of KL divergence. Monte Carlo simulation results indicate that under most of the situations, the model averaging estimators achieves smaller KL divergence in comparison with the existing model selection and averaging methods. In an empirical study with this method, based on the estimation done on the daily volatility of Shanghai Composite Index from June 1st 2016 to June 1st 2017, the model averaging estimators proposed in this paper have produced much accurate results than those from the other available model averaging estimation methods.

Key words: Model Averaging, Nonlinear GARCH Family, Asymptotic Optimality, Realized Volatility