Article

# Systematic analysis of group identification in stock markets.

Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea.
Physical Review E (impact factor: 2.26). 11/2005; 72(4 Pt 2):046133. pp.046133
Source: PubMed

ABSTRACT We propose improved methods to identify stock groups using the correlation matrix of stock price changes. By filtering out the market-wide effect and the random noise, we construct the correlation matrix of stock groups in which nontrivial high correlations between stocks are found. Using the filtered correlation matrix, we successfully identify the multiple stock groups without any extra knowledge of the stocks by the optimization of the matrix representation and the percolation approach to the correlation-based network of stocks. These methods drastically reduce the ambiguities while finding stock groups using the eigenvectors of the correlation matrix.

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##### Article:Uncovering the Internal Structure of the Indian Financial Market: Cross-correlation behavior in the NSE
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ABSTRACT: The cross-correlations between price fluctuations of 201 frequently traded stocks in the National Stock Exchange (NSE) of India are analyzed in this paper. We use daily closing prices for the period 1996-2006, which coincides with the period of rapid transformation of the market following liberalization. The eigenvalue distribution of the cross-correlation matrix, $\mathbf{C}$, of NSE is found to be similar to that of developed markets, such as the New York Stock Exchange (NYSE): the majority of eigenvalues fall within the bounds expected for a random matrix constructed from mutually uncorrelated time series. Of the few largest eigenvalues that deviate from the bulk, the largest is identified with market-wide movements. The intermediate eigenvalues that occur between the largest and the bulk have been associated in NYSE with specific business sectors with strong intra-group interactions. However, in the Indian market, these deviating eigenvalues are comparatively very few and lie much closer to the bulk. We propose that this is because of the relative lack of distinct sector identity in the market, with the movement of stocks dominantly influenced by the overall market trend. This is shown by explicit construction of the interaction network in the market, first by generating the minimum spanning tree from the unfiltered correlation matrix, and later, using an improved method of generating the graph after filtering out the market mode and random effects from the data. Both methods show, compared to developed markets, the relative absence of clusters of co-moving stocks that belong to the same business sector. This is consistent with the general belief that emerging markets tend to be more correlated than developed markets.
04/2007;

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### Keywords

ambiguities

correlation matrix

correlation-based network

eigenvectors

extra knowledge

filtered correlation matrix

market-wide effect

matrix representation

multiple stock groups

percolation approach

stock groups

stock price changes

stocks