Empirical behavior of a world stock index from intra-day to monthly time scales

Most of the papers that study the distributional and fractal properties of financial instruments focus on stock prices or foreign exchange rates. This typically leads to mixed results concerning the distributions of log-returns and some multi-fractal properties of exchange rates, stock prices, and regional indices. This paper uses a well diversified world stock index as the central object of analysis. Such index approximates the growth optimal portfolio, which is demonstrated under the benchmark approach, it is the ideal reference unit for studying basic securities. When denominating this world index in units of a given currency, one measures the movements of the currency against the entire market. This provides a least disturbed observation of the currency dynamics. In this manner, one can expect to disentangle, e.g., the superposition of the two currencies involved in an exchange rate. This benchmark approach to the empirical analysis of financial data allows us to establish remarkable stylized facts. Most important is the observation that the repeatedly documented multi-fractal appearance of financial time series is very weak and much less pronounced than the deviation of the mono-scaling properties from Brownian-motion type scaling. The generalized Hurst exponent H(2) assumes typical values between 0.55 and 0.6. Accordingly, autocorrelations of log-returns decay according to a power law, and the quadratic variation vanishes when going to vanishing observation time step size. Furthermore, one can identify the Studentt distribution as the log-return distribution of a well-diversified world stock index for long time horizons when a long enough data series is used for estimation. The study of dependence properties, finally, reveals that jumps at daily horizon originate primarily in the stock market while at 5min horizon they originate in the foreign exchange market. The principal message of the empirical analysis is that there is evidence that a diffusion model without multi-scaling could reasonably well model the dynamics of a broadly diversified world stock inde

Ornstein-Zernike equation and Percus-Yevick theory for molecular crystals

We derive the Ornstein-Zernike equation for molecular crystals of axially symmetric particles and apply the Percus-Yevick approximation to this system. The one-particle orientational distribution function has a nontrivial dependence on the orientation and is needed as an input. Despite some differences, the Ornstein-Zernike equation for molecular crystals has a similar structure as for liquids. We solve both equations for hard ellipsoids on a sc lattice. Compared to molecular liquids, the tensorial orientational correlators exhibit less structure. However, depending on the lengths a and b of the rotation axis and the perpendicular axes of the ellipsoids, different behavior is found. For oblate and prolate ellipsoids with b >= 0.35 (units of the lattice constant), damped oscillations in distinct directions of direct space occur for some correlators. They manifest themselves in some correlators in reciprocal space as a maximum at the Brillouin zone edge, accompanied by maxima at the zone center for other correlators. The oscillations indicate alternating orientational fluctuations, while the maxima at the zone center originate from nematic-like orientational fluctuations. For a <= 2.5 and b <= 0.35, the oscillations are weaker. For a >= 3.0 and b <= 0.35, no oscillations occur any longer. For many of the correlators in reciprocal space, an increase of a at fixed b leads to a divergence at the zone center q = 0, consistent with nematic-like long range fluctuations, and for some oblate and prolate systems with b ~< 1.0 a simultaneous tendency to divergence of few other correlators at the zone edge is observed. Comparison with correlators from MC simulations shows satisfactory agreement. We also obtain a phase boundary for order-disorder transitions.Comment: 20 pages, 13 figures, submitted to Phys. Rev.

The emerging energy web

There is a general need of elaborating energy-effective solutions for managing our increasingly dense interconnected world. The problem should be tackled in multiple dimensions -technology, society, economics, law, regulations, and politics- at different temporal and spatial scales. Holistic approaches will enable technological solutions to be supported by socio-economic motivations, adequate incentive regulation to foster investment in green infrastructures coherently integrated with adequate energy provisioning schemes. In this article, an attempt is made to describe such multidisciplinary challenges with a coherent set of solutions to be identified to significantly impact the way our interconnected energy world is designed and operated. Graphical abstrac

Quantum Multibaker Maps: Extreme Quantum Regime

We introduce a family of models for quantum mechanical, one-dimensional random walks, called quantum multibaker maps (QMB). These are Weyl quantizations of the classical multibaker models previously considered by Gaspard, Tasaki and others. Depending on the properties of the phases parametrizing the quantization, we consider only two classes of the QMB maps: uniform and random. Uniform QMB maps are characterized by phases which are the same in every unit cell of the multibaker chain. Random QMB maps have phases that vary randomly from unit cell to unit cell. The eigenstates in the former case are extended while in the latter they are localized. In the uniform case and for large $\hbar$, analytic solutions can be obtained for the time dependent quantum states for periodic chains and for open chains with absorbing boundary conditions. Steady state solutions and the properties of the relaxation to a steady state for a uniform QMB chain in contact with ``particle'' reservoirs can also be described analytically. The analytical results are consistent with, and confirmed by, results obtained from numerical methods. We report here results for the deep quantum regime (large $\hbar$) of the uniform QMB, as well as some results for the random QMB. We leave the moderate and small $\hbar$ results as well as further consideration of the other versions of the QMB for further publications.Comment: 17 pages, referee's and editor's comments addresse

Entropy Production, Fractals, and Relaxation to Equilibrium

The theory of entropy production in nonequilibrium, Hamiltonian systems, previously described for steady states using partitions of phase space, is here extended to time dependent systems relaxing to equilibrium. We illustrate the main ideas by using a simple multibaker model, with some nonequilibrium initial state, and we study its progress toward equilibrium. The central results are (i) the entropy production is governed by an underlying, exponentially decaying fractal structure in phase space, (ii) the rate of entropy production is largely independent of the scale of resolution used in the partitions, and (iii) the rate of entropy production is in agreement with the predictions of nonequilibrium thermodynamics

Classical Scattering for a driven inverted Gaussian potential in terms of the chaotic invariant set

We study the classical electron scattering from a driven inverted Gaussian potential, an open system, in terms of its chaotic invariant set. This chaotic invariant set is described by a ternary horseshoe construction on an appropriate Poincare surface of section. We find the development parameters that describe the hyperbolic component of the chaotic invariant set. In addition, we show that the hierarchical structure of the fractal set of singularities of the scattering functions is the same as the structure of the chaotic invariant set. Finally, we construct a symbolic encoding of the hierarchical structure of the set of singularities of the scattering functions and use concepts from the thermodynamical formalism to obtain one of the measures of chaos of the fractal set of singularities, the topological entropy.Comment: accepted in Phy. Rev.

A time series of hydroxylamine (NH2OH) in the southwestern Baltic Sea

Hydroxylamine (NH(2)OH) is an intermediate of the marine nitrogen cycle and in marine environments dissolved NH(2)OH is short-lived. In order to investigate the distribution of NH(2)OH under varying oxygen conditions, its seasonal variability was investigated on a monthly basis from July 2005 to May 2006 at the time series station Boknis Eck located in the Eckernforde Bay (southwestern Baltic Sea). NH(2)OH concentrations were generally low and close to the detection limit. However, a pronounced increase was observed after the seasonal thermohaline stratification period with low oxygen/anoxic conditions in the deep layers was terminated in November 2005. The increase of NH(2)OH was associated with the re-oxygenation of the water column. We conclude that NH(2)OH was produced in-situ during nitrification. We suggest that the detection of significant amounts of NH(2)OH can be used as an indicator for a "fresh" nitrifying system

A multibaker map for shear flow and viscous heating

A consistent description of shear flow and the accompanied viscous heating as well the associated entropy balance is given in the framework of a deterministic dynamical system. A laminar shear flow is modeled by a Hamiltonian multibaker map which drives velocity and temperature fields. In an appropriate macroscopic limit one recovers the Navier-Stokes and heat conduction equations along with the associated entropy balance. This indicates that results of nonequilibrium thermodynamics can be described by means of an abstract, sufficiently chaotic and mixing dynamics. A thermostating algorithm can also be incorporated into this framework.Comment: 11 pages; RevTex with multicol+graphicx packages; eps-figure