We describe a bottom-up framework, based on the identification of appropriate
order parameters and determination of phase diagrams, for understanding
progressively refined agent-based models and simulations of financial markets.
We illustrate this framework by starting with a deterministic toy model,
whereby $N$ independent traders buy and sell $M$ stocks through an order book
that acts as a clearing house. The price of a stock increases whenever it is
bought and decreases whenever it is sold. Price changes are updated by the
order book before the next transaction takes place.
Based on the temporal distributions of clustered segments in the time series
of the ten Dow Jones US (DJUS) economic sector indices, we calculated their
cross correlations over the period February 2000 to August 2008, the two-year
intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 corresponding
segments within the present financial crisis. From these cross-correlation
matrices, we constructed minimal spanning trees (MSTs) of the US economy at the
sector level.
In this paper, we perform a comparative segmentation and clustering analysis
of the time series for the ten Dow Jones US economic sector indices between 14
February 2000 and 31 August 2008. From the temporal distributions of clustered
segments, we find that the US economy took one and a half years to recover from
the mid-1998-to-mid-2003 financial crisis, but only two months to completely
enter the present financial crisis.