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 all MSTs, a core-fringe structure is found, with CY, IN, and NC consistently making up the core, and BM, EN, HC, TL, UT residing predominantly on the fringe. We saw that shocks accompanying volatility movements always start at the fringe, sometimes in conjunction with anomalously high cross correlations here, and propagate inwards to the core of all MSTs of the 11 statistically-stationary corresponding segments. Most of these volatility shocks originate within the domestic fringe sectors, HC, TL, and UT, in the US economy. More importantly, we find that the MSTs can be classified into two distinct, statistically robust, topologies: (i) star-like, with IN at the center, associated with low-volatility economic growth; and (ii) chain-like, associated with high-volatility economic crisis . When we examined successive corresponding segments within the present housing bubble financial crisis, we find that each MST can be obtained from the one before it through a minimal set of primitive rearrangements, each representing a statistically significant change in the cross correlations of the sectors involved . Finally, we present statistical evidence, based on the emergence of a star-like MST in Sep 2009, and the MST staying robustly star-like throughout the Greek Debt Crisis, that the US economy is on track to a recovery.
We calculated the cross correlations between the half-hourly times series of the ten Dow Jones US economic sectors over the period February 2000 to August 2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 segments within the present financial crisis , to construct minimal spanning trees (MSTs) of the US economy at the sector level. In all MSTs, a core-fringe structure is found, with consumer goods, consumer services, and the industrials consistently making up the core, and basic materials, oil and gas, healthcare, telecommunications, and utilities residing predominantly on the fringe. More importantly, we find that the MSTs can be classified into two distinct, statistically robust, topologies: (i) star-like, with the industrials at the center, associated with low-volatility economic growth; and (ii) chain-like, associated with high-volatility economic crisis . Finally, we present statistical evidence, based on the emergence of a star-like MST in Sep 2009, and the MST staying robustly star-like throughout the Greek Debt Crisis, that the US economy is on track to a recovery.
R
Based on the temporal distributions of clustered segments in the time
We calculated the cross correlations between the half-hourly times
R
(DJUS) economic sector indices, we calculated their cross correlations
economic sectors
D
corresponding
R
. From these cross-correlation matrices, we constructed
, to construct
R
CY, IN, and NC
consumer goods, consumer services, and the industrials
R
BM, EN, HC, TL, UT
basic materials, oil and gas, healthcare, telecommunications, and utilities
D
We saw that shocks accompanying volatility movements always start at the fringe, sometimes in conjunction with anomalously high cross correlations here, and propagate inwards to the core of all MSTs of the 11 statistically-stationary corresponding segments. Most of these volatility shocks originate within the domestic fringe sectors, HC, TL, and UT, in the US economy.
R
IN
the industrials
D
. When we examined successive corresponding segments within the present housing bubble financial crisis, we find that each MST can be obtained from the one before it through a minimal set of primitive rearrangements, each representing a statistically significant change in the cross correlations of the sectors involved