Forecasting in Complex Systems

Tuesday, 16 December 2014: 11:20 AM
John B Rundle1,2, James R Holliday2, William R Graves3, Donald L Turcotte1 and Andrea Donnellan4, (1)University of California Davis, Davis, CA, United States, (2)University of California, Davis, CA, United States, (3)Open Hazards Group, Davis, CA, United States, (4)NASA Jet Propulsion Laboratory, Pasadena, CA, United States
Complex nonlinear systems are typically characterized by many degrees of freedom, as well as interactions between the elements. Interesting examples can be found in the areas of earthquakes and finance. In these two systems, fat tails play an important role in the statistical dynamics. For earthquake systems, the Gutenberg-Richter magnitude-frequency is applicable, whereas for daily returns for the securities in the financial markets are known to be characterized by leptokurtotic statistics in which the tails are power law. Very large fluctuations are present in both systems. In earthquake systems, one has the example of great earthquakes such as the M9.1, March 11, 2011 Tohoku event. In financial systems, one has the example of the market crash of October 19, 1987. Both were largely unexpected events that severely impacted the earth and financial systems systemically. Other examples include the M9.3 Andaman earthquake of December 26, 2004, and the Great Recession which began with the fall of Lehman Brothers investment bank on September 12, 2013. Forecasting the occurrence of these damaging events has great societal importance. In recent years, national funding agencies in a variety of countries have emphasized the importance of societal relevance in research, and in particular, the goal of improved forecasting technology. Previous work has shown that both earthquakes and financial crashes can be described by a common Landau-Ginzburg-type free energy model. These metastable systems are characterized by fat tail statistics near the classical spinodal. Correlations in these systems can grow and recede, but do not imply causation, a common source of misunderstanding. In both systems, a common set of techniques can be used to compute the probabilities of future earthquakes or crashes. In this talk, we describe the basic phenomenology of these systems and emphasize their similarities and differences. We also consider the problem of forecast validation and verification. In both of these systems, we show that small event counts (the natural time domain) is an important component of a forecast system.