Detecting Stock Market Fluctuation from Stock Network Structure Variation

We study the structural variation of networks formed by connecting Standard & Poor’s 500 (S&P500) stocks that were traded from January 1, 2000 to December 31, 2004. The construction of the network is based on cross correlation between the time series of the closing prices (or price returns) over a fixed trading period and takes a simple winner-take-all approach for establishing connections between stocks. The period over which the network is constructed is 20 trading days, which should be long enough to produce meaningful cross correlation values, but sufficiently short in order to avoid averaging effects that smooth off the salient fluctuations. A network is constructed for each 20trading-day window in the entire trading period under study. The window moves at a 1-trading-day step. The power-law exponent is determined for each window, along with the corresponding mean error of the power law approximation which reflects how closely the degree distribution resembles a scalefree distribution. The key finding is that the scalefreeness of the degree distribution is disrupted when the market experiences fluctuation. Thus, the mean error of the power-law approximation becomes an effective indicative parameter of the volatility of the stock market.