But again, most of these tests were designed for the low-noise worlds of experimental physics. Analysis of time series in the social sciences often gave indications of previously unanticipated structure, but few or no strong statements could be made about the sort of low-dimensional chaos studied in physics. Much interest focused on the role of chaos in finance, because of the abundance of data and the obvious interest in detecting unknown, predictable patterns. Once again, the tests have indicated the presence of enough nonlinear structure to fuel debates about the predictability of stock prices and foreign exchange rates, but definitive statements about chaos lie well beyond what the data are able to tell us. Much of this failure stems from the fact that chaos tests depend on predictability to some extent.
Many tests monitor short-range forecasts and the speed at which they degrade.
If the degradation happens sufficiently quickly, this behavior can be listed as one of several necessary conditions for chaos. But in financial markets, any observable structure is weak at best, and measuring the precise speed at which a forecast degrades is probably a hopeless task. Although fitting chaotic processes to social-science data series has proved problematic, certain nonlinear time series tools and techniques inspired by chaos have thrived. Chaos served an important role for empirical researchers, reminding them how much structure in a time series could be invisible to the standard linear diagnostics that were in use 15 years ago. In many fields, both physical and social, time series that were thought to be random, or derived from linear dynamics, have been reanalyzed using new, more powerful diagnostics.