Correlation Structures Corresponding to Forward Rates

In finance, there is a constant effort to model future prices of stocks, bonds, and commodities; the ability to predict future behaviour provides important information about the underlying structure of these securities. While it has become common to model a single stock using the Black-Scholes formulation, the modelling of bond prices requires one to simulate the change of interest rates as a function of their maturity, which requires one to model the movement of an entire yield curve. If one studies the spectral decomposition of the correlation matrix corresponding to the spot rates from this curve, then one finds that the top three components can explain nearly all of the data; in addition, this same structure is observed for any bond or commodity. In his 2000 paper, Ilias Lekkos [4] proposes that such results are an artefact due to the implicit correlation between spot rates, and that the analysis should instead be performed using forward rates. In this paper, we discuss the results obtained for the spectral structure of the correlation matrices of forward rates, and investigate a model for this associated structure. The paper is divided into four parts, covering forward rates background material, principal components analysis, yield curve modelling, and conclusions and research extensions

Correlated Binomial Models and Correlation Structures

We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional probabilities. The beta-binomial distribution is derived by a strong symmetric assumption on the conditional correlations. Our derivation clarifies the 'correlation' structure of the beta-binomial distribution. It is also possible to study the correlation structures of other probability distributions of exchangeable (homogeneous) correlated Bernoulli random variables. We study some distribution functions and discuss their behaviors in terms of their correlation structures.Comment: 12 pages, 7 figure

Cross-Correlation of Diffuse Synchrotron and Large-Scale Structures

We explore for the first time the method of cross-correlation of radio synchrotron emission and tracers of large-scale structure in order to detect the diffuse IGM/WHIM. We performed a cross-correlation of a 34 x 34 degree area of 2MASS galaxies for two redshift slices (0.03 < z < 0.04 and 0.06 < z < 0.07) with the corresponding region of the 1.4 GHz Bonn survey. For this analysis, we assumed that the synchrotron surface brightness is linearly proportional to surface density of galaxies. We also sampled the cross-correlation function using 24 distant fields of the same size from the Bonn survey, to better assess the noise properties. Though we obtained a null result, we found that by adding a signal weighted by the 2MASS image with a filament (peak) surface brightness of 1 (7) mK and 7 (49) mK would produce a 3 sigma positive correlation for the 0.03 < z < 0.04 and 0.06 < z < 0.07 redshift slices respectively. These detection thresholds correspond to minimum energy magnetic fields as low as 0.2 microG, close to some theoretical expectations for filament field values. This injected signal is also below the rms noise of the Bonn survey, and demonstrates the power of this technique and its utility for upcoming sensitive continuum surveys such as GALFACTS at Arecibo and those planned with the Murchison Widefield Array (MWA).Comment: 6 pages, 4 figures, accepted to MNRA

Geometrical-topological correlation in structures

The topology of polyhedra, tessellations and networks is described as to their mapping in Schlaefli space. A description of the topological form index is given and it is applied to these structural classes in terms of their geometries

The two-and three-point correlation functions of the polarized five-year WMAP sky maps

We present the two- and three-point real space correlation functions of the five-year WMAP sky maps, and compare the observed functions to simulated LCDM concordance model ensembles. In agreement with previously published results, we find that the temperature correlation functions are consistent with expectations. However, the pure polarization correlation functions are acceptable only for the 33GHz band map; the 41, 61, and 94 GHz band correlation functions all exhibit significant large-scale excess structures. Further, these excess structures very closely match the correlation functions of the two (synchrotron and dust) foreground templates used to correct the WMAP data for galactic contamination, with a cross-correlation statistically significant at the 2sigma-3sigma confidence level. The correlation is slightly stronger with respect to the thermal dust template than with the synchrotron template.Comment: 10 pages, 5 figures, published in ApJ. v2: New title, minor changes to appendix, and fixed some typos. v3: Matches version published in Ap

Periodic correlation structures in bacterial and archaeal complete genomes

The periodic transference of nucleotide strings in bacterial and archaeal complete genomes is investigated by using the metric representation and the recurrence plot method. The generated periodic correlation structures exhibit four kinds of fundamental transferring characteristics: a single increasing period, several increasing periods, an increasing quasi-period and almost noincreasing period. The mechanism of the periodic transference is further analyzed by determining all long periodic nucleotide strings in the bacterial and archaeal complete genomes and is explained as follows: both the repetition of basic periodic nucleotide strings and the transference of non-periodic nucleotide strings would form the periodic correlation structures with approximately the same increasing periods.Comment: 23 pages, 6 figures, 2 table

Correlation functions for extended mass galaxy clusters

The phenomenon of clustering of galaxies on the basis of correlation functions in an expanding Universe is studied by using equation of state, taking gravitational interaction between galaxies of extended nature into consideration. The partial differential equation for the extended mass structures of a two-point correlation function developed earlier by Iqbal, Ahmad and Khan is studied on the basis of assigned boundary conditions. The solution for the correlation function for extended structures satisfies the basic boundary conditions, which seem to be sufficient for understanding the phenomena, and provides a new insight into the gravitational clustering problem for extended mass structures.Comment: 3 pages, no figure