Will the US economy recover in 2010? A minimal spanning tree study

Abstract

a b s t r a c tWe calculated the cross correlations between the half-hourly times series of the ten Dow Jones US economic sectors over the period 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 & 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 starlike 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.

The Japanese Economy in Crises: A Time Series Segmentation Study

“…At the same time, positive sentiments also propagate faster on a 'closer' MST, making this a conducive environment for economic growth. This is in contrast to what we saw in Zhang et al (2011), where we find the US economic MST huddled up during growth (to accelerate it), and opens up during crises (to slow down the spread of contagion). We believe this is the learned response of a mature economy.…”

“…Therefore, their interpretation as the crash phase of the market is unambiguous. In our previous work on the US market Lee et al, 25 Nov 2009;Zhang et al, 2011), and also ongoing study on the European markets, we saw that moderate-volatility green segments are also short, and coincide with periods where the market underwent corrections according to commentators. We therefore associated these as the correction phase, and chose to interpret the longer green time series segments in the Japanese market as evidence for structural differences between Japan and the US/European markets.…”

“…These we further segment, by progressively lowering the threshold ∆ 0 → ∆ 0 < 10 until a segment boundary with strength ∆ > ∆ 0 appears. Based on our previous experiences Lee et al, 25 Nov 2009;Zhang et al, 2011), this semi-automatic recursive segmentation produces acceptable results.…”

Correlation of financial markets in times of crisis

“…This approach was successfully applied to a large number of financial markets [71]- [100], and also to the relation between world markets [101]- [102]. This approach was also used in the construction of hierarchical structures between different assets of financial markets [103]- [142].…”

The Japanese Economy in Crises: A Time Series Segmentation Study

“…Delving deeper into the cross section study, we computed the pairwise Pearson cross correlations between the ten DJUS economic sectors over the two crisis periods, the growth period between them, and also within time series segments of various volatilities (Zhang et al, 2011). Constructing the minimal spanning trees (MSTs) of these cross correlations, we found that the growth sectors such as industrials, consumer goods, and consumer services consistently form the core of the MSTs, whereas quality sectors such as basic materials, oil & gas, healthcare, and utilities frequently reside on the fringe of the MSTs.…”