摘要
在金融市场中，波动率的准确建模和预测是进行资产配置、风险管理等金融
应用的关键。现有的研究主要是基于低频数据的GARCH类模型，但经过大量研究
得出的预测效果却并不稳健。近年来，采用高频数据进行波动率建模备受国内外
学者的青睐，因为其包含了更多的数据信息，但高频数据的市场微观结构噪声、
跳跃等对波动的影响不容忽视。并且传统的低频或高频波动模型的采样频率相
同，这往往限制了变量的选取，可能会降低模型的预测精度。
本文选取沪深300指数日低频数据与5分钟高频数据，将低频GARCH类模型
和高频HAR-RV族、FNN-HAR-J模型相结合，得到混频预测模型——MoP模型。分
别对收益率序列和已实现波动序列进行描述性统计分析，并且对低频波动模型和
高频波动模型进行参数估计，采用 MCS检验法将 GARCH类模型、HAR类模型、
FNN-HAR-J模型以及混频MoP模型进行对比分析。并采用这些模型对金融资产的
动态VaR进行预测。本文的研究具有一定的实践意义，混频波动模型可以进一步
应用于其他金融产品，对防范金融产品的风险有着一定的指导意义。
通过实证分析可得以下结论：首先，通过描述性统计分析，得出收益率序列
和已实现波动序列具有尖峰厚尾性和波动聚集性；通过模型参数估计，发现低频
波动模型中，GARCH模型拟合效果较好，而在高频波动模型中，HAR-RV-CJ模型
拟合效果较好；其次，在MCS检验中，p值越大，模型的预测效果越好。根据MCS
检验，HAR类模型预测效果优于GARCH类模型，另外FNN-HAR-J模型的p值稍大
于 HAR-RV类模型，这可能是因为 FNN-HAR-J模型考虑到了已实现波动 RV的非
线性可能。表现最好的波动预测模型是MoP模型，在所有损失函数情况下，该模
型所对应的p值最大，均为1，其波动预测的准确度最高；再次，与GARCH类模
型相比，高频类预测模型以及MoP模型能够较好的刻画收益率的变动趋势。就大
多数情况而言，VaR的值与收益率的波动呈现正相关。最后，无论是对于多头VaR
还是对于空头VaR的动态预测，在所有模型中，MoP模型对于动态市场风险的预
测效果最好。
关键词：低频波动模型；高频波动模型；混频波动模型；MCS检验；动态VaR
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Abstract
In financial markets, accurate modeling and forecasting of volatility is the key to
financial applications such as asset allocation and risk management. Existing research
is mainly based on GARCH-type models of low-frequency data, but the prediction
effect obtained after a lot of research is not robust. In recent years, the use of
high-frequency data for volatility modeling has been favored by scholars at home and
abroad, because it contains more data information,but the impact of market
microstructure noise and jumps in high-frequency data on volatility cannot be ignored.
And the sampling frequency of traditional low-frequency or high-frequency
fluctuation models is the same, which often limits the selection of variables and may
reduce the prediction accuracy of the model.
In this paper, the daily low-frequency data and 5-minute high-frequency data of
the CSI 300 index are selected, and the low-frequency GARCH model is combined
with the high-frequency HAR-RV family and FNN-HAR-J model to obtain a mixed
frequency prediction model-MoP model. Descriptive statistical analysis is carried out
on the return series and realized volatility series respectively, and the parameters of
the low-frequency fluctuation model and the high-frequency fluctuation model are
estimated, and the GARCH-type model, HAR-type model, FNN-HAR-J model and
The frequency mixing MoP model is compared and analyzed. And use these models
to predict the dynamic VaR of financial assets. The research in this paper has certain
practical significance. The mixed-frequency fluctuation model can be further applied
to other financial products, which has certain guiding significance for preventing the
risks of financial products.
Through empirical analysis, the following conclusions can be drawn: First,
through descriptive statistical analysis, it is concluded that the yield series and
realized volatility series have sharp peaks and thick tails and volatility aggregation;
In the high-frequency fluctuation model, the HAR-RV-CJ model has a better fitting
effect;Second, in the MCS test, the larger the p-value, the better the prediction
performance of the model. According to the MCS test, the prediction effect of the
HAR model is better than that of the GARCH model, and the p-value of the
FNN-HAR-J model is slightly larger than that of the HAR-RV model, which may be
because the FNN-HAR-J model takes into account the realized fluctuation RV.
Nonlinearity possible. The best-performing volatility prediction model is the MoP
model. In all loss functions, the p-value corresponding to this model is the largest,
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which is 1, and its volatility prediction accuracy is the highest;Thirdly, compared with
the GARCH model, the high-frequency forecast model and the MoP model can better
describe the changing trend of returns.For the most part, the value of VaR is positively
correlated with volatility in yields. Finally, for both long VaR and short VaR dynamic
predictions, among all models, the MoP model is the best predictor of dynamic market
risk.
Keywords: Low frequency fluctuation model; High frequency fluctuation model;
Mixed frequency fluctuation model; MCS test; Dynamic VaR
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