Physical approach to complex systems

We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen–Ledoit–Sornette (JLS) model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data. We complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to the most crucial nonlinear parameter, the critical time t c , defined in the JLS model as the end of the bubble and the most probable time for a crash to occur. This further decreases the complexity of the search and provides an intuitive representation of the results of the calibration. With our proposed methodology, metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms, leading to a dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings.

A stable and robust calibration scheme of the log-periodic power law model

. The geomagnetic field is subject to possible reversals or excursions of polarity during its temporal evolution. Considering that: (a) in the last 83 million yr the typical average time between one reversal and the next (the so-called chron) is around 400 000 yr, (b) the last reversal occurred around 780 000 yr ago, (c) more excursions (rapid changes in polarity) can occur within the same chron and (d) the geomagnetic field dipole is currently decreasing, a possible imminent geomagnetic reversal or excursion would not be completely unexpected. In that case, such a phenomenon would represent one of the very few natural hazards that are really global. The South Atlantic Anomaly (SAA) is a great depression of the geomagnetic field strength at the Earth's surface, caused by a reverse magnetic flux in the terrestrial outer core. In analogy with critical point phenomena characterized by some cumulative quantity, we fit the surface extent of this anomaly over the last 400 yr with power law or logarithmic functions in reverse time, also decorated by log-periodic oscillations, whose final singularity (a critical point tc) reveals a great change in the near future (2034 ± 3 yr), when the SAA area reaches almost a hemisphere. An interesting aspect that has recently been found is the possible direct connection between the SAA and the global mean sea level (GSL). That the GSL is somehow connected with SAA is also confirmed by the similar result when an analogous critical-like fit is performed over GSL: the corresponding critical point (2033 ± 11 yr) agrees, within the estimated errors, with the value found for the SAA. From this result, we point out the intriguing conjecture that tc would be the time of no return, after which the geomagnetic field could fall into an irreversible process of a global geomagnetic transition that could be a reversal or excursion of polarity.

/pdf/toward-a-possible-next-geomagnetic-transition-2zf6bgm35z.pdf

Toward a possible next geomagnetic transition

The Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles with finite-time singular crash hazard rates has been developed to describe the dynamics of financial bubbles and crashes. It has been applied successfully to a large variety of financial bubbles in many different markets. Having been developed for more than one decade, the JLS model has been studied, analyzed, used and criticized by several researchers. Much of this discussion is helpful for advancing the research. However, several serious misconceptions seem to be present within this collective conversation both on theoretical and empirical aspects. Several of these problems appear to stem from the fast evolution of the literature on the JLS model and related works. In the hope of removing possible misunderstanding and of catalyzing useful future developments, we summarize these common questions and criticisms concerning the JLS model and offer a synthesis of the existing state-of-the-art and best-practice advices.

Clarifications to Questions and Criticisms on the Johansen-Ledoit-Sornette Bubble Model

Advances in science are being sought in newly available opportunities to collect massive quantities of data about complex systems. While key advances are being made in detailed mapping of systems, how to relate this data to solving many of the challenges facing humanity is unclear. The questions we often wish to address require identifying the impact of interventions on the system and that impact is not apparent in the detailed data that is available. Here we review key concepts and motivate a general framework for building larger scale views of complex systems and for characterizing the importance of information in physical, biological and social systems. We provide examples of its application to evolutionary biology with relevance to ecology, biodiversity, pandemics, and human lifespan, and in the context of social systems with relevance to ethnic violence, global food prices, and stock market panic. Framing scientific inquiry as an effort to determine what is important and unimportant is a means for advancing our understanding and addressing many practical concerns, such as economic development or treating disease.

From Big Data To Important Information

A number of papers claim that a Log Periodic Power Law (LPPL) t- ted to nancial market bubbles that precede large market falls or 'crashes', contain parameters that are conned within certain ranges. The mecha- nism that has been claimed as underlying the LPPL, is based on inuence percolation and a martingale condition. This paper examines these claims and the robustness of the LPPL for capturing large falls in the Hang Seng stock market index, over a 30-year period, including the current global downturn. We identify 11 crashes on the Hang Seng market over the pe-

Fitting the Log Periodic Power Law to financial crashes: a critical analysis

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Fitting the Log Periodic Power Law to financial crashes: a critical analysis