频域分析视角下股票指数波动特征研究

Research on Volatility Characteristics of Stock Index from the Perspective of Frequency Domain Analysis

摘要: 掌握股票指数波动特征是有效管理股市投资风险的重要基础，选择上证指数数据为样本，从频域分析视角，利用希尔伯特–黄变换频域分析方法研究上证指数波动的原因及经济意义。通过分解上证指数，得到不同频率的特征分量，分析原序列内在微观构成特征；通过重构分量，确定影响上证指数波动的高频部分、低频部分和趋势项部分；通过希尔伯特变换，研究其经济意义。实证结果表明，上证指数的波动是高频部分和低频部分共同作用的结果，且上证指数会围绕趋势项部分进行波动。在不同时期，高频部分和低频部分对上证指数波动的贡献程度有所不同，在2007年牛市中，低频部分占据上证指数波动的绝大部分；而在2015年牛市中，上证指数波动的大部分来自于高频部分。研究为投资者管理股市投资风险提供了新的数量依据。

Abstract: To master the volatility characteristics of stock index is an important basis for effective management of stock market investment risk. In this paper, Shanghai Stock Index data is selected as a sample, from the perspective of frequency domain analysis, and the Hilbert-Huang transform frequency domain analysis method is used to study the reasons and economic significance of the volatility of Shanghai Stock index. By decomposing Shanghai Composite index, the characteristic components of different frequencies were obtained, and the intrinsic microscopic composition characteristics of the original sequence were analyzed. By reconstructing component, the high frequency part, low frequency part and trend item part which affect SSE index fluctuation are determined. Through the Hilbert transform, the economic significance is studied. The empirical results show that the fluctuation of the Shanghai Composite Index is the result of the joint action of the high frequency part and the low frequency part, and the Shanghai Composite index will fluctuate around the trend item part. In different periods, the contribution degree of the high frequency part and the low frequency part to the volatility of Shanghai Composite Index varies. In 2007 bull market, the low frequency part occupied the majority of the volatility of Shanghai Composite Index; in the 2015 bull market, most of the volatility of the Shanghai Composite index came from the high-frequency part. This paper provides a new quantitative basis for investors to manage stock market investment risk.