Multiscale Analysis of Complex Time Series: Integration of Chaos and Random Fractal Theory, and Beyond
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Understanding the mechanism of financial crises is an important issue, especially in a time of profound economic difficulty world-wide. To gain insights into how economic crises develop, we examine the exposure network associated with Fannie Mae/Freddie Mac, Lehman Brothers, and American International Group, and show that the losses associated with them can be modeled by an Omori-law-like distribution for earthquake aftershocks. Under certain conditions, Omori's law leads to Pareto distribution. Positive Pareto incomes, together with Omori's law, motivate us to examine whether distributions of negative incomes during crises may also be modeled by Pareto distributions. We find that during crises, negative incomes not only may indeed be modeled as Pareto-like distributions, but actually have heavier tails than those for positive incomes. As a result, entropy flow associated with losses or negative incomes provides an excellent technique for predicting economic downturns.