基于函数型自适应聚类的股票收益波动模式比较

Comparing Returns Volatility Patterns of SSE50 Stock Shares via Functional Adaptive Clustering

股票收益波动具有典型的连续函数特征,将其纳入连续动态函数范畴分析,能够挖掘现有离散分析方法不能揭示的深层次信息。本文基于连续动态函数视角研究上证50指数样本股票收益波动的类别模式和时段特征:首先由实际离散观测数据信息自行驱动,重构隐含在其中的本征收益波动函数;进一步,利用函数型主成分正交分解收益函数波动的主趋势,在无核心信息损失的主成分降维基础上,引入自适应权重聚类分析客观划分股票收益函数波动的模式类别;最后,利用函数型方差分析检验不同类别收益函数之间波动差异的显著性和稳健性,并基于波动函数周期性时段划分、图形展示和可视化剖析每一类别收益函数在不同时段波动的势能转化规律。研究发现:上证综指股票收益波动的主导趋势可以分解为四个子模式,50只股票存在五类显著的波动模式类别,并且五类波动模式的特征差异主要体现在本次研究区间的初始阶段。本文拓展了股票收益波动模式分类和差异因素分析的研究视角,能够为金融监管部门管理策略的制定和证券市场的投资组合配置提供实证支持。

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 timevarying 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.