Abstract: For the key variables of financial market, yield and volatility, based on the high-dimensional state space model, this paper combines EM and sparse algorithms to establish yield network and volatility network among stocks respectively. The yield network depicts the relationship between stock returns, while the volatility network depicts the relationship between stock risks. Compared with existing models, the proposed model can effectively handle high-dimensional time series data. By analyzing the real data in Shenzhen, Shanghai, Hong Kong and New York stock markets, this paper establishes such networks for these four markets. The most prominent result is that the yield network has a higher degree center potential than the volatility network. This paper attributes the above phenomenon to the effect of policy and other factors on yield simple and direct, while the impact on volatility is indirect and complicated. The above results can also serve as the basis for building the multivariate volatility model.

Key words: state space model, ERM algorithm, yield network, volatility network

摘要： 针对金融市场的核心变量——收益率和波动率，基于高维状态空间模型，利用EM和稀疏算法，分别建立了金融产品之间的收益率网络和波动率网络。前者刻画了金融产品收益之间的相互关系，后者刻画了金融产品风险之间的关系。相对于已有模型，上述模型可有效处理高维时间序列数据。对深圳、上海、香港和纽约市场的股票交易数据分析，找出了相应网络结构特征。以上市场的数据分析结果表明，相对于波动率网络，收益率网络具有更高的度数中心势，把这种现象归因于政策等因素对收益率的影响更为直接和简单，而对波动率的影响则是间接和复杂的。上述研究结果也为构建多变量波动率模型提供参考。

关键词: 状态空间模型, ERM算法, 收益率网络, 波动率网络