Log Periodic Power Analysis of Critical Crashes: Evidence from the Portuguese Stock Market

The study of critical phenomena that originated in the natural sciences has been extended to the financial economics’ field, giving researchers new approaches to risk management, forecasting, the study of bubbles and crashes, and many kinds of problems involving complex systems with self-organized criticality (SOC). This study uses the theory of self-similar oscillatory time singularities to analyze stock market crashes. We test the Log Periodic Power Law/Model (LPPM) to analyze the Portuguese stock market, in its crises in 1998, 2007, and 2015. Parameter values are in line with those observed in other markets. This is particularly interesting since if the model performs robustly for Portugal, which is a small market with liquidity issues and the index is only composed of 20 stocks, we provide consistent evidence in favor of the proposed LPPM methodology. The LPPM methodology proposed here would have allowed us to avoid big loses in the 1998 Portuguese crash, and would have permitted us to sell at points near the peak in the 2007 crash. In the case of the 2015 crisis, we would have obtained a good indication of the moment where the lowest data point was going to be achieved.

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Self-organized criticality and stock market dynamics: an empirical study

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2004.11.061 ◽

2005 ◽

Vol 350 (2-4) ◽

pp. 451-465 ◽

Cited By ~ 17

Author(s):

M. Bartolozzi ◽

D.B. Leinweber ◽

A.W. Thomas

Keyword(s):

Stock Market ◽

Empirical Study ◽

Market Dynamics ◽

Self Organized ◽

Self Organized Criticality

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DYNAMICAL EXPLANATION FOR THE EMERGENCE OF POWER LAW IN A STOCK MARKET MODEL

International Journal of Modern Physics C ◽

10.1142/s0129183196000077 ◽

1996 ◽

Vol 07 (01) ◽

pp. 65-72 ◽

Cited By ~ 74

Author(s):

MOSHE LEVY ◽

SORIN SOLOMON ◽

GIVAT RAM

Keyword(s):

Stock Market ◽

Power Law ◽

Wealth Distribution ◽

Power Laws ◽

Stationary Regime ◽

Market Model ◽

Self Organized ◽

Wide Range ◽

Self Organized Criticality ◽

Sand Piles

Power laws are found in a wide range of different systems: From sand piles to word occurrence frequencies and to the size distribution of cities. The natural emergence of these power laws in so many different systems, which has been called self-organized criticality, seems rather mysterious and awaits a rigorous explanation. In this letter we study the stationary regime of a previously introduced dynamical microscopic model of the stock market. We find that the wealth distribution among investors spontaneously converges to a power law. We are able to explain this phenomenon by simple general considerations. We suggest that similar considerations may explain self-organized criticality in many other systems. They also explain the Levy distribution.

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Harmonic dynamics of the abelian sandpile

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1812015116 ◽

2019 ◽

Vol 116 (8) ◽

pp. 2821-2830 ◽

Cited By ~ 1

Author(s):

Moritz Lang ◽

Mikhail Shkolnikov

Keyword(s):

Abelian Group ◽

Stochastic Dynamics ◽

Third Order ◽

Infinite Domains ◽

Self Organized ◽

Abelian Sandpile ◽

Self Organized Criticality ◽

Self Similar ◽

Smooth Transformation ◽

Sandpile Group

The abelian sandpile is a cellular automaton which serves as the archetypical model to study self-organized criticality, a phenomenon occurring in various biological, physical, and social processes. Its recurrent configurations form an abelian group, whose identity is a fractal composed of self-similar patches. Here, we analyze the evolution of the sandpile identity under harmonic fields of different orders. We show that this evolution corresponds to periodic cycles through the abelian group characterized by the smooth transformation and apparent conservation of the patches constituting the identity. The dynamics induced by second- and third-order harmonics resemble smooth stretchings and translations, respectively, while the ones induced by fourth-order harmonics resemble magnifications and rotations. Based on an extensive analysis of these sandpile dynamics on domains of different size, we conjecture the existence of several scaling limits for infinite domains. Furthermore, we show that the space of harmonic functions provides a set of universal coordinates identifying configurations between different domains, which directly implies that the sandpile group admits a natural renormalization. Finally, we show that the harmonic fields can be induced by simple Markov processes and that the corresponding stochastic dynamics show remarkable robustness. Our results suggest that harmonic fields might split the sandpile group into subsets showing different critical coefficients and that it might be possible to extend the fractal structure of the identity beyond the boundaries of its domain.

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The role of self-organization during confined comminution of granular materials

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2009.0205 ◽

2010 ◽

Vol 368 (1910) ◽

pp. 231-247 ◽

Cited By ~ 76

Author(s):

Oded Ben-Nun ◽

Itai Einav

Keyword(s):

Fractal Dimension ◽

Granular Materials ◽

Power Law ◽

Self Organization ◽

Self Organized ◽

Self Organized Criticality ◽

Self Similar ◽

Discrete Element Simulations ◽

Comprehensive Study

During confined comminution of granular materials a power-law grain size distribution (gsd) frequently evolves. We consider this power law as a hint for fractal topology if self-similar patterns appear across the scales. We demonstrate that this ultimate topology is mostly affected by the rules that define the self-organization of the fragment subunits, which agrees well with observations from simplistic models of cellular automata. There is, however, a major difference that highlights the novelty of the current work: here the conclusion is based on a comprehensive study using two-dimensional ‘crushable’ discrete-element simulations that do not neglect physical conservation laws. Motivated by the paradigm of self-organized criticality, we further demonstrate that in uniaxial compression the emerging ultimate fractal topology, as given by the fractal dimension, is generally insensitive to alteration of global index properties of initial porosity and initial gsd. Finally, we show that the fractal dimension in the confined crushing systems is approached irrespective of alteration of the criteria that define when particles crush.

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Self-Similar Criticality

Fractals ◽

10.1142/s0218348x03002117 ◽

2003 ◽

Vol 11 (03) ◽

pp. 221-231 ◽

Cited By ~ 1

Author(s):

Sarah F. Tebbens ◽

Stephen M. Burroughs

Keyword(s):

Power Law ◽

Similar Distribution ◽

Scaling Exponent ◽

Cumulative Frequency ◽

Size Distributions ◽

Scaling Exponents ◽

Natural Systems ◽

Self Organized ◽

Self Organized Criticality ◽

Self Similar

Cumulative frequency-size distributions associated with many natural phenomena follow a power law. Self-organized criticality (SOC) models have been used to model characteristics associated with these natural systems. As originally proposed, SOC models generate event frequency-size distributions that follow a power law with a single scaling exponent. Natural systems often exhibit power law frequency-size distributions with a range of scaling exponents. We modify the forest fire SOC model to produce a range of scaling exponents. In our model, uniform energy (material) input produces events initiated on a self-similar distribution of critical grid cells. An event occurs when material is added to a critical cell, causing that material and all material in occupied non-diagonal adjacent cells to leave the grid. The scaling exponent of the resulting cumulative frequency-size distribution depends on the fractal dimension of the critical cells. Since events occur on a self-similar distribution of critical cells, we call this model Self-Similar Criticality (SSC). The SSC model may provide a link between fractal geometry in nature and observed power law frequency-size distributions for many natural systems.

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Self-organized criticality: Does it have anything to do with criticality and is it useful?

Nonlinear Processes in Geophysics ◽

10.5194/npg-8-193-2001 ◽

2001 ◽

Vol 8 (4/5) ◽

pp. 193-196 ◽

Cited By ~ 20

Author(s):

D. L. Turcotte

Keyword(s):

Forest Fires ◽

Mantle Convection ◽

Deterministic Chaos ◽

Diffusion Limited Aggregation ◽

Self Organized ◽

Diffusion Limited ◽

Self Organized Criticality ◽

Self Similar ◽

Similarities And Differences ◽

And Diffusion

Abstract. Three aspects of complexity are fractals, chaos, and self-organized criticality. There are many examples of the applicability of fractals in solid-earth geophysics, such as earthquakes and landforms. Chaos is widely accepted as being applicable to a variety of geophysical phenomena, for instance, tectonics and mantle convection. Several simple cellular-automata models have been said to exhibit self-organized criticality. Examples include the sandpile, forest fire and slider-blocks models. It is believed that these are directly applicable to landslides, actual forest fires, and earthquakes, respectively. The slider-block model has been shown to clearly exhibit deterministic chaos and fractal behaviour. The concept of self-similar cascades can explain self-organized critical behaviour. This approach also illustrates the similarities and differences with critical phenomena through association with the site-percolation and diffusion-limited aggregation models.

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Sandpile Models and Solar Flares: Eigenfunction Decomposition for Data Assimilation

Proceedings of the International Astronomical Union ◽

10.1017/s1743921317007244 ◽

2017 ◽

Vol 13 (S335) ◽

pp. 250-253

Author(s):

Antoine Strugarek ◽

Allan S. Brun ◽

Paul Charbonneau ◽

Nicole Vilmer

Keyword(s):

Data Assimilation ◽

Solar Flares ◽

Similar Distribution ◽

Significant Challenge ◽

Self Organized ◽

Self Organized Criticality ◽

Model Independent ◽

Self Similar ◽

Sandpile Models ◽

Data Assimilation Technique

AbstractThe largest solar flares, of class X and above, are often associated with strong energetic particle acceleration. Based on the self-similar distribution of solar flares, self-organized criticality models such as sandpiles can be used to successfully reproduce their statistics. However, predicting strong (and rare) solar flares turns out to be a significant challenge. We build here on an original idea based on the combination of minimalistic flare models (sandpiles) and modern data assimilation techniques (4DVar) to predict large solar flares. We discuss how to represent a sandpile model over a reduced set of eigenfunctions to improve the efficiency of the data assimilation technique. This improvement is model-independent and continues to pave the way towards efficient near real-time solutions for predicting solar flares.

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Problem behavior in autism spectrum disorders: A paradigmatic self-organized perspective of network structures

Behavioral and Brain Sciences ◽

10.1017/s0140525x18001188 ◽

2019 ◽

Vol 42 ◽

Author(s):

Lucio Tonello ◽

Luca Giacobbi ◽

Alberto Pettenon ◽

Alessandro Scuotto ◽

Massimo Cocchi ◽

...

Keyword(s):

Autism Spectrum Disorder ◽

Problem Behaviors ◽

Autism Spectrum ◽

The Self ◽

Network Structures ◽

Self Organized ◽

Critical Equilibrium ◽

Self Organized Criticality ◽

Acute Agitation ◽

Spectrum Disorders

AbstractAutism spectrum disorder (ASD) subjects can present temporary behaviors of acute agitation and aggressiveness, named problem behaviors. They have been shown to be consistent with the self-organized criticality (SOC), a model wherein occasionally occurring “catastrophic events” are necessary in order to maintain a self-organized “critical equilibrium.” The SOC can represent the psychopathology network structures and additionally suggests that they can be considered as self-organized systems.

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