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.Comment: 10 pages, 4 figures, to appear in the Proceedings of the International Workshop on Econophysics of Stock Markets and Minority Games, Calcutta, 200

Heisenberg frustrated magnets: a nonperturbative approach

Frustrated magnets are a notorious example where the usual perturbative methods are in conflict. Using a nonperturbative Wilson-like approach, we get a coherent picture of the physics of Heisenberg frustrated magnets everywhere between $d=2$ and $d=4$. We recover all known perturbative results in a single framework and find the transition to be weakly first order in $d=3$. We compute effective exponents in good agreement with numerical and experimental data.Comment: 5 pages, Revtex, technical details available at http://www.lpthe.jussieu.fr/~tissie

Fractional derivatives of random walks: Time series with long-time memory

We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying autocorrelation functions. The relation between these correlated walks and the well-known fractionally integrated autoregressive (FIGARCH) models, commonly used in econometric studies, is discussed. The application of correlated random walks to simulate empirical financial times series is considered and compared with the predictions from FIGARCH and the simpler FIARCH processes. A comparison with empirical data is performed.Comment: 10 pages, 14 figure

Liquidity and the multiscaling properties of the volume traded on the stock market

We investigate the correlation properties of transaction data from the New York Stock Exchange. The trading activity f(t) of each stock displays a crossover from weaker to stronger correlations at time scales 60-390 minutes. In both regimes, the Hurst exponent H depends logarithmically on the liquidity of the stock, measured by the mean traded value per minute. All multiscaling exponents tau(q) display a similar liquidity dependence, which clearly indicates the lack of a universal form assumed by other studies. The origin of this behavior is both the long memory in the frequency and the size of consecutive transactions.Comment: 7 pages, 3 figures, submitted to Europhysics Letter

Tricritical behavior of the frustrated XY antiferromagnet

Extensive histogram Monte-Carlo simulations of the XY antiferromagnet on a stacked triangular lattice reveal exponent estimates which strongly favor a scenario of mean-field tricritical behavior for the spin-order transition. The corresponding chiral-order transition occurs at the same temperature but appears to be decoupled from the spin-order. These results are relevant to a wide class of frustrated systems with planar-type order and serve to resolve a long-standing controversy regarding their criticality.Comment: J1K 2R1 4 pages (RevTex 3.0), 4 figures available upon request, Report# CRPS-94-0

Analysis methods for collaborative models and activities

Abstract. A classification of analysis methods for CSCL systems is presented which uses as one dimension the distinction into summary analysis and structural analysis and as another distinction different types of raw data: either user actions or state descriptions. The Cool Modes environment for collaborative modeling enables us to explore the whole spectrum of analysis methods. Action logging is based on the MatchMaker communication server underlying Cool Modes. Example instances for several analysis methods have been implemented in the Cool Modes framework.

Epsilon Expansion for Multicritical Fixed Points and Exact Renormalisation Group Equations

The Polchinski version of the exact renormalisation group equations is applied to multicritical fixed points, which are present for dimensions between two and four, for scalar theories using both the local potential approximation and its extension, the derivative expansion. The results are compared with the epsilon expansion by showing that the non linear differential equations may be linearised at each multicritical point and the epsilon expansion treated as a perturbative expansion. The results for critical exponents are compared with corresponding epsilon expansion results from standard perturbation theory. The results provide a test for the validity of the local potential approximation and also the derivative expansion. An alternative truncation of the exact RG equation leads to equations which are similar to those found in the derivative expansion but which gives correct results for critical exponents to order $\epsilon$ and also for the field anomalous dimension to order $\epsilon^2$. An exact marginal operator for the full RG equations is also constructed.Comment: 40 pages, 12 figures version2: small corrections, extra references, final appendix rewritten, version3: some corrections to perturbative calculation

Improved tensor-product expansions for the two-particle density matrix

We present a new density-matrix functional within the recently introduced framework for tensor-product expansions of the two-particle density matrix. It performs well both for the homogeneous electron gas as well as atoms. For the homogeneous electron gas, it performs significantly better than all previous density-matrix functionals, becoming very accurate for high densities and outperforming Hartree-Fock at metallic valence electron densities. For isolated atoms and ions, it is on a par with previous density-matrix functionals and generalized gradient approximations to density-functional theory. We also present analytic results for the correlation energy in the low density limit of the free electron gas for a broad class of such functionals.Comment: 4 pages, 2 figure

A natural orbital functional for the many-electron problem

The exchange-correlation energy in Kohn-Sham density functional theory is expressed as a functional of the electronic density and the Kohn-Sham orbitals. An alternative to Kohn-Sham theory is to express the energy as a functional of the reduced first-order density matrix or equivalently the natural orbitals. In the former approach the unknown part of the functional contains both a kinetic and a potential contribution whereas in the latter approach it contains only a potential energy and consequently has simpler scaling properties. We present an approximate, simple and parameter-free functional of the natural orbitals, based solely on scaling arguments and the near satisfaction of a sum rule. Our tests on atoms show that it yields on average more accurate energies and charge densities than the Hartree Fock method, the local density approximation and the generalized gradient approximations