Extracting Market Trends from the Cross Correlation between Stock Time Series

• Published in: Advanced Techniques for Knowledge Engineering and Innovative Applications pp. 25 - 38
• Main Authors: Tanaka-Yamawaki, Mieko, Yang, X., Kido, T., Yamamoto, A.
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2013
• Series: Communications in Computer and Information Science
• Subjects: Cross correlation matrix; Eigenvector components; Quarterly trends in the stock market; RMT-PCA
• ISBN: 9783642420160; 3642420168
• ISSN: 1865-0929; 1865-0937
• DOI: 10.1007/978-3-642-42017-7_3

In this paper, the RMT-PCA is applied on daily-close stock prices of American Stocks in NYSE for 16 years from 1994 to 2009 to show the effectiveness and consistency of this method by analyzing the whole data of 16 years at once, as well as analyzing the cut data in various lengths between 2-8 years. The extracted trends are consistent to the actual history of the markets. The authors further analyze the intra-day stock prices of Tokyo Stock Market for 12 quarters extending from 2007 to 2009 and attempted to answer to the two remaining question of the RMT-PCA. 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. While the second issue is still open, the authors have found for the first issue 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. This paper argues 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 time period. The authors also discuss on the problem of setting the effective border between the noise and signals considering the artificial correlation created in the process of taking log-returns in analyzing the price time series.