Trend Switching Processes in Financial Markets

Abstract

For an intriguing variety of switching processes in nature, the underlying complex system abruptly changes at a specific point from one state to another in a highly discontinuous fashion. Financial market fluctuations are characterized by many abrupt switchings creating increasing trends (“bubble formation”) and decreasing trends (“bubble collapse”), on time scales ranging from macroscopic bubbles persisting for hundreds of days to microscopic bubbles persisting only for very short time scales. Our analysis is based on a German DAX Future data base containing 13,991,275 transactions recorded with a time resolution of 10^{− 2} s. For a parallel analysis, we use a data base of all S&P500 stocks providing 2,592,531 daily closing prices. We ask whether these ubiquitous switching processes 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 features similar to those present in phase transitions. We find that the well-known catastrophic bubbles that occur on large time scales – such as the most recent financial crisis – are no outliers but in fact single dramatic representatives caused by the formation of upward and downward trends on time scales varying over nine orders of magnitude from the very large down to the very small.