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传统的函数型GARCH族模型可用于刻画函数型金融时间序列的异方差性，但其存在以下局限性，如未考虑波动率的非对称性，不能解释当前信息对未来条件方差的冲击是否存在持续性，参数非负的约束条件可能会限制条件波动率的动态变化。基于此，本文在EGARCH模型的基础上构建了函数型EGARCH模型（f EGARCH模型），给出了其最小二乘估计和拟极大似然估计方法的具体步骤，推导了f EGARCH模型的函数型信息冲击曲线（NIC）和函数型累积冲击响应比率函数（CIRR）的计算公式。蒙特卡洛模拟结果表明，f EGARCH模型能够捕捉非对称性，且其拟极大似然估计方法比最小二乘估计方法更为有效。将该模型应用于沪深300指数，NIC显示该模型能够捕捉波动率的非对称性，而CIRR表明当前收益率对未来波动率的影响存在高持续性。最后，拟极大似然估计值的DM检验以及基于稳健损失函数的SPA检验和MCS检验结果均表明，f EGARCH模型比函数型GARCH模型（f GARCH模型）具有更高的波动预测精度。
Abstract：The traditional functional GARCH-type models can be used to describe the heteroscedasticity of functional financial time series, but they have the following drawbacks: Firstly, they don't consider the asymmetry of volatility; Secondly, they can not explain whether the shock of current information to future conditional variance persists or not; Thirdly, the condition of non-negative parameter may limit the dynamics of conditional volatility. Considering these, this paper, on the basis of EGARCH model, proposes a functional EGARCH model(f EGARCH model), gives the specific steps of its least square estimation and quasi-maximum likelihood estimation, and derives the news impact curve(NIC) and formula of cumulative impact response ratio function(CIRR). Monte Carlo simulation shows that the model can capture the asymmetry, and its quasi-maximum likelihood method is more effective than the least square estimation method. After we apply f EGARCH to CSI 300 index, NIC shows that the model can capture the asymmetry of volatility, and CIRR indicates that the impact of current returns on future volatility is highly persistent. Finally, the DM test based on quasi-maximum likelihood, the SPA test and the MCS test based on several robust loss functions show that the f EGARCH model has better prediction accuracy than the functional GARCH model(f GARCH model).
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基本信息:
DOI：10.19343/j.cnki.11-1302/c.2022.05.011
中图分类号:O212.1;F832.51
引用信息:
[1]蔡光辉,吴志敏.函数型EGARCH模型的构建及其波动预测研究[J].统计研究,2022,39(05):146-160.DOI:10.19343/j.cnki.11-1302/c.2022.05.011.
基金信息:
国家社会科学基金项目“高频金融数据统计测度模型的拓展研究”（19BTJ013）; 浙江省重点建设高校优势特色学科（浙江工商大学统计学）资助项目; 统计数据工程技术与应用协同创新中心资助项目
2022-04-28
2022-04-28
2022-04-28