Switching phenomena in a system with no switches

Abstract

It is widely believed that switching phenomena require switches, but this is actually not true. For an intriguing variety of switching phenomena in nature, the underlying complex system abruptly changes from one state to another in a highly discontinuous fashion. For example, financial market fluctuations are characterized by many abrupt switchings creating increasing trends ("bubble formation") and decreasing trends ("financial collapse"). Such switching occurs on time scales ranging from macroscopic bubbles persisting for hundreds of days to microscopic bubbles persisting only for a few seconds. We analyze a database containing 13,991,275 German DAX Future transactions recorded with a time resolution of 10 msec. For comparison, a database providing 2,592,531 of all S&P500 daily closing prices is used. We ask whether these ubiquitous switching phenomena have quantifiable features independent of the time horizon studied. We find striking scale-free behavior of the volatility after each switching occurs. We interpret our findings as being consistent with time-dependent collective behavior of financial market participants. We test the possible universality of our result by performing a parallel analysis of fluctuations in transaction volume and time intervals between trades. We show that these financial market switching processes have properties similar to those of phase transitions. We suggest that the well-known catastrophic bubbles that occur on large time scales-such as the most recent financial crisis-are no outliers but single dramatic representatives caused by the switching between upward and downward trends on time scales varying over nine orders of magnitude from very large (≈102 days) down to very small (≈10 ms). © Springer Science+Business Media, LLC 2009.