Universal characteristics of financial phase transitions |
Stanisław Drożdż ^{1,2}, Frank Grümmer ^{3}, Jarosław Kwapień ^{1}, Josef Speth ^{3} |
1. Polish Academy of Sciences, Institute of Nuclear Physics (IFJ PAN), Radzikowskiego 152, Kraków 31-342, Poland |
Abstract |
The financial world seems to constitute the most complex system in Nature. The phenomena underlying its dynamics comprise essentially all the elements and interactions that are associated with life, both on the individual as well as on the social level. Typical for such systems is a permanent competition between noise and collectivity. In fact it apparently is noise that overwhelms. Collectivity is much more subtle and fragile as it is connected with a significant reduction of dimensionality, but it is collectivity which is of primary interest because it makes patterns and allows the constituents to be identifiable by sharing some common properties. The financial dynamics is a multiscale phenomenon and therefore the question which of its properties are scale invariant and which are scale characteristic refers to the essence of this phenomenon. There exists evidence that at least a large portion of the financial dynamics is governed by phenomena analogous to criticality in the statistical physics sense. In its conventional form criticality implies a continuous scale invariance in terms of the standard power-law. The financial dynamics seems to be governed by a generalisation of this concept such that the conventional dominating scaling acquires a correction that is periodic in the logarithm of the distance from the critical time. Such points coincide thus with the accumulation of oscillations and it is this effect that can potentially be used for prediction. An important related element, for a proper interpretation and handling of the financial patterns as well as for consistency of the theory, is that such log-periodic patterns manifest their action self-similarly for various time-scales. This applies both to the accelerating bubble and to the decelerating anti-bubble market phases. Another crucial element is identification that the preferred scaling factor is the same through all the time scales and markets. This fact significantly amplifies the predictive power of the corresponding methodology as compared to other methods presented so far in the literature. We provide several further examples of the financial dynamics that can be consistently decomposed into transparent log-periodic components. |