Correlation patterns of NIKKEI index constituents: Towards a mean-field model

An analysis of minute-tick data from the Japanese stock index market is reported for a three-year period of 2000/7/4–2003/6/30. Correlation patterns and principal component distributions were determined for 180 constituents of the NIKKEI 225 index, excluding the effects of after-hours trading and constituent revisions. The first principal component describes about 30% of the total variance in constituent log returns (subject to slow decrease with the size of the correlation window), suggesting that a small number of physical parameters may describe the internal dynamics of the index, allowing for an adiabatic representation of index dynamics, and a self-consistent mean-field model of its constituents. Finally, it is shown that the introduction of a time gap into minute-tick data significantly improves the correlations of the price-weighed index with its constituents, even when such gap inserts are strictly penalized. This phenomenon corresponds to a heterogenous response time of index constituents to the adiabatic collective motion and also demonstrates the inhomogeneous nature of equidistant time ticks in financial trading.