The statistical properties of technical trading rules

A portfolio of 200 heterogeneous technical trading rules is tested for their directional predictabilities on the DJIAI from 1988 to 1999. We also explore several nonparametric techniques designed for brain research, and detected possibly other forms of dependencies more significant than the traditional linear autocorrelation for the time series. The overall conditional mean directional predictability is 46%. 36 percent of the rules have more than 50% directional predictability, and the top 20 percent rules has a 73% directional predictability, whereas the bottom 80 percent has a directional predictability of 40%. Buy signals consistently generate higher predictability than sell signals but do not commensurate with their respective risk levels. The relationship between two sub-periods is not stable, while the difference between the conditional mean directional predictability of buy only and sell only signals is highly significance. The belief that most successful rules have a directional predictability of 25% to 50% coincides with the mode of distribution. We observe counter intuitive relationship between volatility and directional predictability. The results of directional predictability in a downtrend concur with the argument that buy-and-hold strategy is not a suitable benchmark. Attempts are made to tackle the issues of small sample bias, data snooping, size of test window, bootstrap or t-test, and homogeneity. Issues are discussed on empirical testing for their real world applications, statistical and non-statistical interpretations; also randomness test; physical or biological science approach

Use of Amendments to Reduce Water Requirements for Stand Establishment of Small-Seeded Crops

Soil crusting after planting is a serious problem in stand establishment of small-seeded crops in the Southwest. When crusting occurs in a saline, warm soil, stand establishment problems are especially severe. It is customary to use costly irrigation water to keep seedbed surfaces moist after planting to reduce soil crusting and to lower soil temperatures. Phosphoric acid (24% and 12%) and sulfuric acid (95%) were evaluated to determine their effectiveness in reducing soil crusting and reducing the amount of water required to obtain stands of sugarbeets, alfalfa, wheat and barley. Phosphoric acid, applied in 4-6 cm bands over the seed row at planting and before irrigation, reduced crusting and increased sugarbeet and alfalfa seedling emergence. Emerged seedlings from phosphoric acid treated plots were larger and one irrigation (10-15 ha cm/ha) was saved in stand establishment. Sulfuric acid applied in bands reduced soil crusting. Soluble salts in the seed zone resulting from band application of sulfuric acid killed or damaged seedlings. Sulfuric acid, when applied in irrigation water to saline-sodic soils, improved plant growth and water use efficiency

Vortex lines of the electromagnetic field

Relativistic definition of the phase of the electromagnetic field, involving two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110 (2000)] of the motion of vortex lines embedded in the solutions of wave equations from Schroedinger wave mechanics to Maxwell theory. It is shown that time evolution of vortex lines has universal features; in Maxwell theory it is very similar to that in Schroedinger wave mechanics. Connection with some early work on geometrodynamics is established. Simple examples of solutions of Maxwell equations with embedded vortex lines are given. Vortex lines in Laguerre-Gaussian beams are treated in some detail.Comment: 11 pages, 6 figures, to be published in Phys. Rev.

Iso-singlet Down Quark Mixing And CP Violation Experiments

We confront the new physics models with extra iso-singlet down quarks in the new CP violation experimental era with $\sin{(2\beta)}$ and $\epsilon'/\epsilon$ measurements, $K^+ \to \pi^+ \nu \bar{\nu}$ events, and $x_s$ limits. The closeness of the new experimental results to the standard model theory requires us to include full SM amplitudes in the analysis. In models allowing mixing to a new isosinglet down quark, as in E$_6$, flavor changing neutral currents are induced that allow a $Z^0$ mediated contribution to $B-\bar B$ mixing and which bring in new phases. In $(\rho,\eta)$, $(x_s,\sin{(\gamma)})$, and $(x_s, \sin{(2\phi_s)})$ plots we still find much larger regions in the four down quark model than in the SM, reaching down to $\eta \approx 0$, $0 \leq \sin{(\gamma)} \leq 1$, $-.75 \leq \sin{(2\alpha)} \leq 0.15$, and $\sin{(2\phi_s)}$ down to zero, all at 1$\sigma$. We elucidate the nature of the cancellation in an order $\lambda^5$ four down quark mixing matrix element which satisfies the experiments and reduces the number of independent angles and phases. We also evaluate tests of unitarity for the $3\times3$ CKM submatrix.Comment: 14 pages, 16 figures, REVTeX

Tunneling and propagation of vacuum bubbles on dynamical backgrounds

In the context of bubble universes produced by a first-order phase transition with large nucleation rates compared to the inverse dynamical time scale of the parent bubble, we extend the usual analysis to non-vacuum backgrounds. In particular, we provide semi-analytic and numerical results for the modified nucleation rate in FLRW backgrounds, as well as a parameter study of bubble walls propagating into inhomogeneous (LTB) or FLRW spacetimes, both in the thin-wall approximation. We show that in our model, matter in the background often prevents bubbles from successful expansion and forces them to collapse. For cases where they do expand, we give arguments why the effects on the interior spacetime are small for a wide range of reasonable parameters and discuss the limitations of the employed approximations.Comment: 29 pages, 8 figures, typos corrected, matches published versio

On the fourth-order accurate compact ADI scheme for solving the unsteady Nonlinear Coupled Burgers' Equations

The two-dimensional unsteady coupled Burgers' equations with moderate to severe gradients, are solved numerically using higher-order accurate finite difference schemes; namely the fourth-order accurate compact ADI scheme, and the fourth-order accurate Du Fort Frankel scheme. The question of numerical stability and convergence are presented. Comparisons are made between the present schemes in terms of accuracy and computational efficiency for solving problems with severe internal and boundary gradients. The present study shows that the fourth-order compact ADI scheme is stable and efficient

Spinodal Decomposition in a Binary Polymer Mixture: Dynamic Self Consistent Field Theory and Monte Carlo Simulations

We investigate how the dynamics of a single chain influences the kinetics of early stage phase separation in a symmetric binary polymer mixture. We consider quenches from the disordered phase into the region of spinodal instability. On a mean field level we approach this problem with two methods: a dynamical extension of the self consistent field theory for Gaussian chains, with the density variables evolving in time, and the method of the external potential dynamics where the effective external fields are propagated in time. Different wave vector dependencies of the kinetic coefficient are taken into account. These early stages of spinodal decomposition are also studied through Monte Carlo simulations employing the bond fluctuation model that maps the chains -- in our case with 64 effective segments -- on a coarse grained lattice. The results obtained through self consistent field calculations and Monte Carlo simulations can be compared because the time, length, and temperature scales are mapped onto each other through the diffusion constant, the chain extension, and the energy of mixing. The quantitative comparison of the relaxation rate of the global structure factor shows that a kinetic coefficient according to the Rouse model gives a much better agreement than a local, i.e. wave vector independent, kinetic factor. Including fluctuations in the self consistent field calculations leads to a shorter time span of spinodal behaviour and a reduction of the relaxation rate for smaller wave vectors and prevents the relaxation rate from becoming negative for larger values of the wave vector. This is also in agreement with the simulation results.Comment: Phys.Rev.E in prin

A shooting algorithm for problems with singular arcs

In this article we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method is used to compute a zero of the shooting function. This shooting algorithm is locally quadratically convergent if the derivative of the shooting function is one-to-one at the solution. The main result of this paper is to show that the latter holds whenever a sufficient condition for weak optimality is satisfied. We note that this condition is very close to a second order necessary condition. For the case when the shooting system can be reduced to one having the same number of unknowns and equations (square system) we prove that the mentioned sufficient condition guarantees the stability of the optimal solution under small perturbations and the invertibility of the Jacobian matrix of the shooting function associated to the perturbed problem. We present numerical tests that validate our method.Comment: No. RR-7763 (2011); Journal of Optimization, Theory and Applications, published as 'Online first', January 201