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金融时间序列的波动性建模经历了从一阶矩到二阶矩直到高阶矩(包含三阶矩和四阶矩)的过程,而对于高阶矩波动模型是否有助于对未来市场的波动率预测这一问题,国内外学术界尚无文献讨论。以上证综指长达7年的每5分钟高频数据样本为例,通过构建具有不同矩属性的波动模型,计算了中国股票市场波动率的预测值,并利用具有bootstrap特性的SPA检验法,实证检验了不同矩属性波动模型的波动率预测精度差异。实证结果显示:就中国股市而言,四阶矩波动模型能够取得比二阶矩波动模型更优的波动率预测精度,而三阶矩波动模型并未表现出比二阶矩波动模型更强的预测能力;在高阶矩波动模型中包含杠杆效应项并不能提高模型的预测精度。最后提出了在金融风险管理、衍生产品定价等领域引入四阶矩波动模型的研究思路。
The modeling of the volatility of the financial time series has gone through the process from the first moment to the second moment until the higher moment (including the third moment and the fourth moment), but whether the higher moment volatility model is helpful to the future market Volatility forecast this problem, there is no literature discussion at home and abroad. Take the 5-minute high-frequency data samples of the Shanghai Composite Index up to 7 years as an example, this paper calculates the forecast value of the volatility of the Chinese stock market by constructing a volatility model with different moment properties. By using SPA test with bootstrap feature, Empirical test of different moments of volatility model volatility prediction accuracy difference. Empirical results show that for the Chinese stock market, the fourth-moment volatility model can achieve better forecasting accuracy than the second-order moment volatility model, while the third-order moment volatility model does not show any stronger performance than the second-order moment volatility model Prediction ability. Including the leverage effect term in the high-order moment fluctuation model does not improve the prediction accuracy of the model. Finally, the author puts forward the research ideas of introducing the fourth moment volatility model in the fields of financial risk management and derivative pricing.