arXiv subjects

Janos Kertesz

Publications and source records attributed to Janos Kertesz.

At least 55 records · Page 3Linked to original sources

arXiv2006

Why do Hurst exponents of traded value increase as the logarithm of company size?

The common assumption of universal behavior in stock market data can sometimes lead to false conclusions. In statistical physics, the Hurst exponents characterizing long-range correlations are often closely related to universal exponents. We show, that in the case of time series of the traded value, these Hurst exponents increase logarithmically with company size, and thus are non-universal. Moreover, the average transaction size shows scaling with the mean transaction frequency for large enough companies. We present a phenomenological scaling framework that properly accounts for such dependencies.

physics.soc-ph↗

arXiv2005

Limitations of scaling and universality in stock market data

We present evidence, that if a large enough set of high resolution stock market data is analyzed, certain analogies with physics -- such as scaling and universality -- fail to capture the full complexity of such data. Despite earlier expectations, the mean value per trade, the mean number of trades per minute and the mean trading activity do not show scaling with company capitalization, there is only a non-trivial monotonous dependence. The strength of correlations present in the time series of traded value is found to be non-universal: The Hurst exponent increases logarithmically with capitalization. A similar trend is displayed by intertrade time intervals. This is a clear indication that stylized facts need not be fully universal, but can instead have a well-defined dependence on company size.

physics.soc-ph↗

arXiv2005

The effect of disorder on the hierarchical modularity in complex systems

We consider a system hierarchically modular, if besides its hierarchical structure it shows a sequence of scale separations from the point of view of some functionality or property. Starting from regular, deterministic objects like the Vicsek snowflake or the deterministic scale free network by Ravasz et al. we first characterize the hierarchical modularity by the periodicity of some properties on a logarithmic scale indicating separation of scales. Then we introduce randomness by keeping the scale freeness and other important characteristics of the objects and monitor the changes in the modularity. In the presented examples sufficient amount of randomness destroys hierarchical modularity. Our findings suggest that the experimentally observed hierarchical modularity in systems with algebraically decaying clustering coefficients indicates a limited level of randomness.

cond-mat.stat-mech↗

arXiv2005

Force indeterminacy in the jammed state of hard disks

Granular packings of hard discs are investigated by means of contact dynamics which is an appropriate technique to explore the allowed force-realizations in the space of contact forces. Configurations are generated for given values of the friction coefficient, and then an ensemble of equilibrium forces is found for fixed contacts. We study the force fluctuations within this ensemble. In the limit of zero friction the fluctuations vanish in accordance with the isostaticity of the packing. The magnitude of the fluctuations has a non-monotonous friction dependence. The increase for small friction can be attributed to the opening of the angle of the Coulomb cone, while the decrease as friction increases is due to the reduction of connectivity of the contact-network, leading to local, independent clusters of indeterminacy. We discuss the relevance of indeterminacy to packings of deformable particles and to the mechanical response properties.

cond-mat.soft↗

arXiv2005

Increasing market efficiency: Evolution of cross-correlations of stock returns

We analyse the temporal changes in the cross correlations of returns on the New York Stock Exchange. We show that lead-lag relationships between daily returns of stocks vanished in less than twenty years. We have found that even for high frequency data the asymmetry of time dependent cross-correlation functions has a decreasing tendency, the position of their peaks are shifted towards the origin while these peaks become sharper and higher, resulting in a diminution of the Epps effect. All these findings indicate that the market becomes increasingly efficient.

physics.soc-ph↗

arXiv2005

Non-trivial scaling of fluctuations in the trading activity of NYSE

Complex systems comprise a large number of interacting elements, whose dynamics is not always a priori known. In these cases -- in order to uncover their key features -- we have to turn to empirical methods, one of which was recently introduced by Menezes and Barabasi. It is based on the observation that for the activity f_i(t) of the constituents there is a power law relationship between the standard deviation and the mean value: sigma_i ~ ^alpha. For stock market trading activity (traded value), good scaling over 5 orders of magnitude with the exponent alpha = 0.72 was observed. The origin of this non-trivial scaling can be traced back to a proportionality between the rate of trades and their mean sizes . One finds ~ ^0.69 for the ~1000 largest companies of New York Stock Exchange. Model independent calculations show that these two types of scaling can be mapped onto each other, with an agreement between the error bars. Finally, there is a continuous increase in alpha if we look at fluctuations on an increasing time scale up to 20 days.

physics.soc-ph↗

arXiv2005

Random walks on complex networks with inhomogeneous impact

In many complex systems, for the activity f(i) of the constituents or nodes i, a power-law relationship was discovered between the standard deviation sigma(i) and the average strength of the activity: sigma(i) ~ ^alpha; universal values alpha = 1/2 or 1 were found, however, with exceptions. With the help of an impact variable we introduce a random walk model where the activity is the product of the number of visitors at a node and their impact. If the impact depends strongly on the node connectivity and the properties of the carrying network are broadly distributed (like in a scale free network) we find both analytically and numerically non-universal alpha values. The exponent always crosses over to the universal value of 1 if the external drive dominates.

cond-mat.stat-mech↗

arXiv2005

Spatial snowdrift game with myopic agents

We have studied a spatially extended snowdrift game, in which the players are located on the sites of two-dimensional square lattices and repeatedly have to choose one of the two strategies, either cooperation (C) or defection (D). A player interacts with its nearest neighbors only, and aims at playing a strategy which maximizes its instant pay-off, assuming that the neighboring agents retain their strategies. If a player is not content with its current strategy, it will change it to the opposite one with probability $p$ next round. Here we show through simulations and analytical approach that these rules result in cooperation levels, which differ to large extent from those obtained using the replicator dynamics.

physics.bio-ph↗

arXiv2004

Multiscaling and non-universality in fluctuations of driven complex systems

For many externally driven complex systems neither the noisy driving force, nor the internal dynamics are a priori known. Here we focus on systems for which the time dependent activity of a large number of components can be monitored, allowing us to separate each signal into a component attributed to the external driving force and one to the internal dynamics. We propose a formalism to capture the potential multiscaling in the fluctuations and apply it to the high frequency trading records of the New York Stock Exchange. We find that on the time scale of minutes the dynamics is governed by internal processes, while on a daily or longer scale the external factors dominate. This transition from internal to external dynamics induces systematic changes in the scaling exponents, offering direct evidence of non-universality in the system.

cond-mat.stat-mech↗

arXiv2004

Short-term market reaction after extreme price changes of liquid stocks

In our empirical study, we examine the price of liquid stocks after experiencing a large intraday price change using data from the NYSE and the NASDAQ. We find significant reversal for both intraday price decreases and increases. The results are stable against varying parameters. While on the NYSE the large widening of the bid-ask spread eliminates most of the profits that can be achieved by a contrarian strategy, on the NASDAQ the bid-ask spread stays almost constant yielding significant short-term abnormal profits. Furthermore, volatility, volume, and in case of the NYSE the bid-ask spread, which increase sharply at the event, decay according to a power-law and stay significantly high over days afterwards.

cond-mat.other↗

arXiv2004

Multifractal model of asset returns with leverage effect

Multifractal processes are a relatively new tool of stock market analysis. Their power lies in the ability to take multiple orders of autocorrelations into account explicitly. In the first part of the paper we discuss the framework of the Lux model and refine the underlying phenomenological picture. We also give a procedure of fitting all parameters to empirical data. We present a new approach to account for the effective length of power-law memory in volatility. The second part of the paper deals with the consequences of asymmetry in returns. We incorporate two related stylized facts, skewness and leverage autocorrelations into the model. Then from Monte Carlo measurements we show, that this asymmetry significantly increases the mean squared error of volatility forecasts. Based on a filtering method we give evidence on similar behavior in empirical data.

cond-mat.other↗

arXiv2004

The effect of contact torques on porosity of cohesive powders

The porosity of uniaxially compacted cohesive powders depends on the applied stress (including gravity). The case, where these stresses are weak, is considered. The compaction results in a porosity which is a function of sliding, rolling and torsion friction. By contact dynamics simulations it is shown that the influences of contact torques (static rolling and torsion friction) on the porosity are significant and approximately additive. The relevance for nano-powder pressure sintering is discussed.

cond-mat.soft↗

arXiv2004

Phase Diagram of Optimal Paths

We show that choosing appropriate distributions of the randomness, the search for optimal paths links diverse problems of disordered media like directed percolation, invasion percolation, directed and non-directed spanning polymers. We also introduce a simple and efficient algorithm, which solves the d-dimensional model numerically in order N^(1+d_f/d) steps where d_f is the fractal dimension of the path. Using extensive simulations in two dimensions we identify the phase boundaries of the directed polymer universality class. A new strong-disorder phase occurs where the optimum paths are self-affine with parameter-dependent scaling exponents. Furthermore, the phase diagram contains directed and non-directed percolation as well as the directed random walk models at specific points and lines.

cond-mat.stat-mech↗

arXiv2002

The contact dynamics method for granular media

In this paper we review the simulation method of the non-smooth contact dynamics. This technique was designed to solve the unilateral and frictional contact problem for a large number of rigid bodies and has proved to be especially valuable in research of dense granular materials during the last decade. We present here the basic principles compared to other methods and the detailed description of a 3D algorithm. We point out an artifact manifesting itself in spurious sound waves and discuss the applicability of the method.

cond-mat.soft↗

arXiv2002

Shearing of loose granular materials: A statistical mesoscopic model

A two-dimensional lattice model for the formation and evolution of shear bands in granular media is proposed. Each lattice site is assigned a random variable which reflects the local density. At every time step, the strain is localized along a single shear-band which is a spanning path on the lattice chosen through an extremum condition. The dynamics consists of randomly changing the `density' of the sites only along the shear band, and then repeating the procedure of locating the extremal path and changing it. Starting from an initially uncorrelated density field, it is found that this dynamics leads to a slow compaction along with a non-trivial patterning of the system, with high density regions forming which shelter long-lived low-density valleys. Further, as a result of these large density fluctuations, the shear band which was initially equally likely to be found anywhere on the lattice, gets progressively trapped for longer and longer periods of time. This state is however meta-stable, and the system continues to evolve slowly in a manner reminiscent of glassy dynamics. Several quantities have been studied numerically which support this picture and elucidate the unusual system-size effects at play.

cond-mat.stat-mech↗

arXiv2002

Slow relaxation due to optimization and restructuring: Solution on a hierarchical lattice

Motivated by the large strain shear of loose granular materials we introduced a model which consists of consecutive optimization and restructuring steps leading to a self organization of a density field. The extensive connections to other models of statistical phyics are discussed. We investigate our model on a hierarchical lattice which allows an exact asymptotic renormalization treatment. A surprisingly close analogy is observed between the simulation results on the regular and the hierarchical lattices. The dynamics is characterized by the breakdown of ergodicity, by unusual system size effects in the development of the average density as well as by the age distribution, the latter showing multifractal properties.

cond-mat.stat-mech↗

arXiv2002

Structural transitions in scale-free networks

Real growing networks like the WWW or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the (Barabasi-Albert) preferential attachment network growth capture all these aspects. We present a scaling theory to describe the behavior of the generalized models and the mean field rate equation for the problem. This is solved for a specific case with the result C(k) ~ 1/k for the clustering of a node of degree k. Numerical results agree with such a mean-field exponent which also reproduces the clustering of many real networks.

cond-mat.stat-mech↗

arXiv2002

Shortest paths and load scaling in scale-free trees

The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function (pdf) of the distances may take various forms. Here we analyze these by considering mean-field arguments and by mapping the m=1 case of the Barabasi-Albert model into a tree with a depth-dependent branching ratio. This shows the origins of the average distance scaling and allows a demonstration of why the distribution approaches a Gaussian in the limit of N large. The load (betweenness), the number of shortest distance paths passing through any node, is discussed in the tree presentation.

cond-mat.stat-mech↗