Recent analysis of truly huge quantities of empirical data suggests that classic economic theories not only fail for a few outliers, but that there occur similar outliers of every possible size. Specifically, if we analyze only a small data set (say 104 data points), then outliers appear to occur as “rare events.” However, when we analyze four orders of magnitude more data (108 data points), we find four orders of magnitude more outliers—so ignoring them is not a responsible option. We find that the statistical properties of these “outliers” are identical to the statistical properties of everyday fluctuations.
Two unifying principles that underlie much of the finance analysis we will present are scale invariance and universality. Scale invariance is a property not about algebraic equations but rather about functional equations, which have as their solutions not numbers but rather functional forms—e.g., the solution of the functional equation
f(λ x)=λp f(x)
is f(x)=xp. The key idea of universality is that the identical set of “scaling laws” hold across diverse markets, and over diverse time periods.
We demonstrate the principles of scaling and universality by describing very recent work. Financial market fluctuations are characterized by many abrupt switchings on very short time scales, from increasing “microtrends” to decreasing “microtrends”—and vice versa. We ask whether these ubiquitous switching processes have quantifiable features analogous to those present in phase transitions, and find striking scale-free behavior of the time intervals between transactions both before and after the switching occurs.
Recent disasters ranging from financial “shocks” to large-scale terrorist attacks dramatically exemplify the fact that the most dangerous vulnerability is hiding in the many interdependencies among different networks. Specifically, we have uncovered new empirical laws governing the nature of switching phenomena in coupled networks, and found that phenomena that are continuous “second order” phase transitions in isolated networks become discontinuous abrupt “first order” transitions in interdependent networks. We find that the same laws governing the formation and bursting of the largest financial bubbles also govern the tiniest finance bubbles, over a factor of 1,000,000,000 in time scale.
Finally, we analyze changes in Google query volumes for search terms related to finance and find patterns that may be early warning signs of stock market moves. We conclude by discussing the network basis for understanding sudden death in the elderly, and the possibility that financial “flash crashes” are not unlike the catastrophic first-order failure incidents occurring in interdependent networks.
This work was carried out in collaboration with a number of colleagues, most especially T. Preis, H.S. Moat, S. Havlin and S.V. Buldyrev.