Zhaoyuan Li, Maozai Tian

【Abstract】

In this paper, we propose a new method to classify the stock cluster based on the motions of stock returns. Specifically, there are three criteria: (1) The positive or negative signs of elements in the eigenvector of correlation matrix indicate the response direction of individual stocks. (2) The components are included based on the sequence of corresponding eigenvalue magnitudes from large to small. (3) All the elements in the cluster representing individual stocks should have same signs across the components included in the classification process. With the number of vectors included in the process increasing, a speed-up process for cluster number is identified. We interpret this phenomenon as a phase transition from a state dominated by meaningful information to one dominated by trivial information. And a critical point exists in this process. The sizes of clusters near this critical point can be regarded as a power law distribution. The critical exponent evolvement indicates structure of the market. The vector number at this point can be adopted to classify the stock clusters. We analyze the cross-correlation matrices of stock logarithm returns of both China and US stock market for the period from January 4, 2005 to December 31, 2010. The period includes the anomalies time of financial crisis. The number of clusters in financial and technology sectors is further examined to reveal the varying feather of traditional industries. Distinct patterns of industrial differentiation between China and US have been found according to our study.

【Keywords】

generalized estimating equations, local polynomial kernel regression, varying-coefficient models, working correlation matrix