Chaos Analysis Use in Forecasting

Chaos is a field of investigation that attempts to identify underlying order in situations that appear disorderly. A system in chaos exhibit fractal behavior; that is, features of the system are repetitive at all scales. A system in chaos has these qualitative characteristics: 1)Involves feedback paths and some recursive or non-linear elements. 2)Forecasting with accuracy beyond chance is difficult or impossible. 3)Is either unresponsive to external forces or very sensitive to external forces. The system is very sensitive to initial conditions. An organizing force (attractor) exists in some plane that leads to the random-appearing system performance. But even with these guidelines, identification is certain only if we know a priori that a random appearing time series has been produced by a deterministic relationship. There are also quantitative methods for identifying chaotic conditions of dynamic systems. Some methods use a Poincaré map, which is "the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower dimensional subspace, called the Poincaré section, transversal to the flow of the system". There are several possible means for “de-escalating” chaotic situations such as: 1)Slow things down, interfere with the feedback. 2)A “kick in the pants” strategy. This approach requires applying a nudge at just the right time and place. 3)Control from the bottom up. 4)Accommodate it. 5)Add capacity. 6)Time the feedback. 7)Add noise. Strengths and Weaknesses. There is a significant gap between the qualitative and quantitative approaches to detecting chaos in dynamic systems. While real-life systems can be diagnosed as being in chaos through observing noise-like behavior and other characteristics, it is difficult to distinguish between random and chaotic behavior. The mathematical approach requires advanced analysis techniques not likely to be available to most futurists. Furthermore, on the theoretical side, many systems of interest cannot as yet be described in terms of dynamic equations and are in any event difficult to bound.