Extracting Quarterly Trends of Tokyo Stock Market by Means of RMT-PCA

摘要

We attempt to clarify two remaining issues in the RMT-PCA, a recently developed tool to extract trendy industrial sectors in a stock market based on the comparison of the eigenvalue spectrum of the cross correlation matrix between pairs of stock price time series to the theoretical spectrum derived from RMT. The first issue is the number of principal components to examine, and the second issue is the number of eminent elements to examine out of the total N components of the chosen eigenvectors. In order to answer to those questions, we have analyzed the intra-day stock prices of Tokyo Stock Market for 12 quarters extending from 2007 to 2009. To the first issue, we found that only the second largest principal component is sufficient to examine, based on the comparison of this scenario and the use of the largest ten principal components. We argue on this point that the positive elements, and the negative elements, of the eigenvector components individually form collective modes of industrial sectors in the second eigenvector U2, and those collective modes reveal themselves as trendy sectors of the market in that season. To the second issue, we have not reached any conclusion and simply compare the two scenarios. The first scenario is to pick ten largest elements from the positive components and another ten from the negative components, and the second scenario is to pick the accumulated 20% elements from the combination of positive and negative elements. The quarterly trends obtained from both scenarios are consistent to the yearly trends and the historical events in general.