关键词: 函数型主成分, 波动模式, 自适应聚类, 上证50

Abstract: There is a typical character of continuous function existing in the volatility of stock shares. If analyzing its trajectory under continuous dynamic function domain, we can excavate more in-depth information, which cannot be revealed by the existing discrete analysis. The paper exploits the category patterns and time-varying characteristics of returns volatility of sample shares in Shanghai stock exchange 50 index (SSE50) based on the continuous dynamic functional perspective. Firstly, to construct the intrinsic volatility function driven by information implied in actual discrete observation. Further, to decompose the dominant mode of returns volatility function orthogonally using functional principal components. Thirdly, to perform adaptive weight clustering analysis on the fluctuation mode of stock returns based on the dimensionality reduction of principal components without losing core information. Lastly, to test the robustness and significance of difference among different volatility patterns via functional analysis of variance, then display graphically and analyze visually groups' potential energy transformation rule in different intervals based on periodic divisions. The Empirical results show: 1) the dominant mode of returns volatility function of SSE50 can be divided into four sub-models. 2) 50 sample stock shares have five kinds of significant volatility patterns. 3) The characteristic differences of five volatility patterns are all reflected at the initial stage of this research interval. This paper expands the research perspective by classifying returns volatility modes of stock shares and analyzing difference factors, which can be the empirical support for the financial regulatory department to formulate management strategy and for the stock market to allocate portfolio.

Key words: Functional Principal Component, Volatility Patterns, Adaptive Clustering, SSE50