基于最小一乘准则的上证指数突变点研究

很多研究表明,上证指数序列既有结构突变的特征,也有厚尾的特征。但大部分现有的研究都没有考虑其厚尾特征对变点估计的影响。本文基于最小一乘准则提出了一个估计厚尾数据中变点的方法。模拟研究表明,当数据具有厚尾特征时,基于最小一乘准则的变点估计比基于最小二乘准则的估计有效。对上证指数的实证结果表明,基于最小一乘准则估计出的变点能更好地描述中国股票市场的结构突变特征。

Study of Change Points in Shanghai Composite Index Based on Least Absolute Deviation Criterion

The series of Shanghai Composite Index not only has structural changes, but also is heavy-tailed. For example, the kurtosis of log returns of its daily closing prices from 2006/1/4 to 2011/12/31 is 5.61. It is much greater than that of the normal distribution, so the log returns data are heavy-tailed obviously. Moreover, the stock market in this period experienced the switchover from a big bull market to a big bear market, which will lead to many structural changes. However, the most existing studies did not consider the influence of the heavy-tailed feature on the estimation of change points. To solve this problem, an approach was proposed in this paper to estimate change points in heavy-tailed data based on the least absolute deviation criterion, which is more robust than least squares criterion and can fit data with heavy-tailed feature well. The results obtained from simulation studies showed that the estimates of the number and locations of change points based on the least absolute deviation criterion are more accurate than those based on least square criterion when the simulated data have heavy-tailed feature. This shows that the former is more efficient than the latter. The log returns of daily closing prices of Shanghai Composite Index from 2006/1/4 to 2011/12/31 were collected for empirical study. The empirical results indicated that the change points estimated by least absolute deviation criterion are different from those estimated by least squares criterion, and the former can describe the structural changes of Chinese stock market well. Hence, the results obtained from the simulated studies and empirical analysis show that it is necessary to consider the heavy-tailed feature in estimating structural changes when the data have heavy-tailed feature.