Order Moments Research Articles

Higher-order moment risk spillovers and optimal portfolio strategies in global oil markets

Investigating the dynamic interdependencies and risk connectedness in global oil markets is paramount for investors and regulatory bodies. Nevertheless, prevailing research has predominantly focused on the examination of lower-order moments, thereby imposing limitations on the extent of inquiry. This paper undertakes an analysis of higher-order moment risk spillovers in global oil markets employing the innovative time-varying parameter vector autoregression (TVP-VAR) extended joint connectedness approach. Moreover, this study pioneers the construction of minimum connectedness portfolio strategies encompassing oil markets worldwide, incorporating the outcomes of higher-order moment risk connectedness into multivariate portfolio construction. Our empirical investigation unequivocally highlights the ascendance of OPEC oil as the preeminent net transmitter of connectedness across all moments, reinforcing its pivotal role in the transmission of risk. Furthermore, our findings disclose significant heterogeneity in the connectedness outcomes, with discernible variations across diverse moment orders. Remarkably, the oil benchmarks of WTI and Brent undergo a discernible transformation, transitioning into net recipients when subjected to higher-order moment risk spillovers. Additionally, the dynamics of equicorrelations, pairwise correlations, as well as the time-varying total, net, and net-pairwise connectedness indices, exhibit a high degree of responsiveness to major crisis events. Finally, the incorporation of higher-order moment risk spillovers into oil portfolio strategies manifests enhanced efficacy in risk management. The policy implications derived from our findings bear practical significance for an array of stakeholders, including cross-market investors, portfolio managers, regulatory entities, and policymakers.

Integrating in-situ multi-modal characterizations with signatures to investigate localized deformation

Multi-modal approaches are often essential for exploring the intricate facets of complex materials phenomena. Each characterization technique contributes a unique perspective that, when linked with other techniques, enables a more holistic and comprehensive study. Sometimes direct interpretations of material response between techniques become infeasible, necessitating the use of indirect interpretations or signatures to build a complete understanding. In this work, we present a case study that combines signature discovery with electron and synchrotron X-ray characterization techniques to identify regions of intense slip localization - a complex material phenomenon - via a signature within an Inconel-718 alloy undergoing mechanical deformation. This signature relies on the higher order moments of single grain orientation distributions, which prove sensitive to localized deformation. We report the intergranular stress states within a grain neighborhood identified through this signature.

Almost sharp weighted Sobolev trace inequalities in the unit ball under constraints

In this paper, we establish some improved weighted Sobolev trace inequalities [Formula: see text] under the zero higher order moments constraint via the concentration compactness principle, where [Formula: see text] is a defining function of [Formula: see text] and [Formula: see text]. This relates to the fractional (conformal) Laplacians and related problems in conformal geometry. We construct some test functions and show that the inequality is almost optimal when [Formula: see text].

Conditions for finiteness and bounds on moments of generalized order statistics

We present necessary and sufficient conditions for the finiteness of moments of a fixed order of generalized order statistics based on an arbitrary life baseline distribution with a finite expectation. The conditions depend on a relation between the moment order and the minimal parameter of the generalized order statistic and its multiplicity. Furthermore, under these conditions we determine sharp upper bounds on the moments of generalized order statistic expressed in the scale units being the respective powers of the mean of the baseline distribution.

A new bivariate distribution with uniform marginals

Starting from three independent exponential random variables we have generated a bivariate random vector (U, V) having the marginal distributions as standard uniform. The joint distribution function and the survival function have been derived along with the moment generating function. We have also given an expression for the joint moment of order (r, s). The distributions of different functions of U and V have been derived. Different dependence measures between U and V have also been calculated. The reliability of the underlying stress-strength model has been obtained as an application of the distribution. A simulation exercise has been carried out to check for the goodness-of-fit of the model. We have also calculated the relative errors in different reliability measures under the assumption that the variables U and V are independent when actually they are not.

Graph transformer-based self-adaptive malicious relation filtering for fraudulent comments detection in social network

In recent years, Graph Neural Networks (GNNs) have proven to be effective in detecting fraud within social networks by gathering information from neighboring nodes to predict fraudulent actions. However, the continuous evolution and camouflaging tactics of fraudsters, such as establishing malicious connections with legitimate users and mimicking their behaviors, can often elude GNN-based detection methods. To tackle this issue, we propose a multi-order moments graph transformer, named MMGT, to effectively learn node representations through an attention mechanism that captures information of different orders of moments. Building upon this foundation, we further introduce a self-adaptive malicious relation filtering model for fraud detection, denoted as SFGT. Initially, we form a multi-relational graph that encapsulates complex relations within a given social network and derive node representations by accumulating neighbor node and edge data based on an enhanced graph transformer. Subsequently, a threshold-based malicious relation filter mechanism is proposed to eliminate malicious links by assessing the distance between nodes. Furthermore, an adaptive threshold learning policy is developed to bolster the model’s performance and its ability to generalize. Finally, extensive experiments are carried out on two public datasets, Amazon and YelpChi, which underscores the effectiveness of our proposed model. The experimental results indicate that our model achieves state-of-the-art performance.

The Problem of Moments: A Bunch of Classical Results with Some Novelties

We summarize significant classical results on (in)determinacy of measures in terms of their finite positive integer order moments. Well known is the role of the smallest eigenvalues of Hankel matrices, starting from Hamburger’s results a century ago and ending with the great progress made only in recent times by C. Berg and collaborators. We describe here known results containing necessary and sufficient conditions for moment (in)determinacy in both Hamburger and Stieltjes moment problems. In our exposition, we follow an approach different from that commonly used. There are novelties well complementing the existing theory. Among them are: (a) to emphasize on the geometric interpretation of the indeterminacy conditions; (b) to exploit fine properties of the eigenvalues of perturbed symmetric matrices allowing to derive new lower bounds for the smallest eigenvalues of Hankel matrices (these bounds are used for concluding indeterminacy); (c) to provide new arguments to confirm classical results; (d) to give new numerical illustrations involving commonly used probability distributions.

Magnetic ordering in the layered oxyhalide Sr2NiO2Cl2

The full characterisation of the high-pressure-synthesised, metastable layered oxyhalide Sr2NiO2Cl2 is reported. It is comprised of infinite NiO2 layers along with double rock salt Sr2Cl2 layers and is closely related to the n = 1 Ruddlesden-Popper phases. At ambient temperature, it crystallises in the tetragonal space group I4/mmm with 2 formula units per unit cell with the basal lattice parameters a = b = 4.03417(2) Å and the stacking direction lattice parameter, c = 15.1058(1) Å. A tiny cusp in the temperature dependence of the magnetic susceptibility in a previous report suggested that this oxyhalide underwent long-range magnetic order and therefore contained high-spin Ni2+ ions. Powder neutron diffraction has confirmed that Sr2NiO2Cl2 is a localised-moment oxyhalide, adopting the high-spin S = 1 configuration with fully occupied dxz, dyz and dxy orbitals and partially occupied dz2 and dx2-y2 orbitals. The Ni2+ magnetic moments order antiferromagnetically below ≈ 180 K in a G-type arrangement on a √2a × √2a × c expansion of the nuclear cell with the propagation vector (½, ½, 0) and with a saturated long-range ordered magnetic moment of 1.57(7) μB per Ni2+ cation which is in line with previously calculated computational results and showing that the ligand field around the Ni2+ cation is not sufficiently anisotropic to drive it into the low-spin, diamagnetic configuration found for this d8 cation in square planar or highly elongated octahedral coordination.

Overview of mathematical background of homogenization, summary of method MASH and comments on benchmark validation

AbstractThere are several methods and software for the homogenization of climate data series but there is not any exact mathematical theory of homogenization. As we see, the basic problem of homogenization is the unreasonable dominance of the practical procedures over the theory. Therefore we try to formulate some questions of homogenization in accordance with the mathematical conventions. The topics to be discussed are as follows. (a) Themes and systems—meteorological, mathematical and software links. (b) Mathematical formulation of climate data series homogenization and special case of normal distribution. (c) Additive and multiplicative spatiotemporal models for climate data series homogenization. (d) Mathematical overview of methodological questions as, spatial comparison of series, inhomogeneity detection and adjustment of series, in accordance with the WMO Guidelines on Homogenisation (2020). (e) The last topic is the new version of MASH for homogenization of mean and standard deviation. The earlier versions of our method MASH (Multiple Analysis of Series for Homogenization; Szentimrey) were developed formerly at the Hungarian Meteorological Service. These procedures aimed to homogenize the daily and monthly data series in the mean, that is, the first order moment. The new version MASHv4.01 has been developed for joint homogenization of mean and standard deviation using some mathematical results. Theoretically, in case of normal distribution, the homogenization of mean and standard deviation is sufficient since if the first two moments are homogenous then the higher order moments are also homogeneous. An interactive automatic algorithm also was developed in this new version in order to make the homogenization easier for the users. We will present a summary of the software MASH where our intention was to develop a flexible, interactive automatic, artificial intelligence (AI) system. We finish the paper with some comments connected to the theoretical evaluation and benchmark validation of the methods.

Convergence of genealogies through spinal decomposition with an application to population genetics

Consider a branching Markov process with values in some general type space. Conditional on survival up to generation N, the genealogy of the extant population defines a random marked metric measure space, where individuals are marked by their type and pairwise distances are measured by the time to the most recent common ancestor. In the present manuscript, we devise a general method of moments to prove convergence of such genealogies in the Gromov-weak topology when N rightarrow infty . Informally, the moment of order k of the population is obtained by observing the genealogy of k individuals chosen uniformly at random after size-biasing the population at time N by its kth factorial moment. We show that the sampled genealogy can be expressed in terms of a k-spine decomposition of the original branching process, and that convergence reduces to the convergence of the underlying k-spines. As an illustration of our framework, we analyse the large-time behavior of a branching approximation of the biparental Wright–Fisher model with recombination. The model exhibits some interesting mathematical features. It starts in a supercritical state but is naturally driven to criticality. We show that the limiting behavior exhibits both critical and supercritical characteristics.

Gamma-shadowed two-ray with diffuse power composite fading model

In this paper, a novel gamma-shadowed two-ray with diffuse power (GS-TWDP) composite fading model is proposed by assuming that the shadowing-caused mean power variations of the received signal, affected by TWDP multipath fading, are gamma distributed. For the proposed model, the essential statistics such as probability density function (PDF), cumulative distribution function (CDF), moment generating function (MGF) and higher order moments are obtained and used to derive the approximate general order rectangular quadrature amplitude (RQAM) average symbol error probability (ASEP). That expression enabled us to investigate the effect of shadowing on overall error probability, in case when signal is propagating in channels with TWDP multipath fading. The proposed model is verified by comparing analytically obtained results with those measured at 28 GHz and reported in literature, which makes the GS-TWDP model a promising candidate for modeling propagation at millimeter wave (mmWave) frequencies. Analytical results are validated by Monte-Carlo simulation.

Bonding mechanism and magnetic ordering in Laves phase λ1−MgCo2 intermetallic compound from theoretical and experimental studies

In the present work we have studied the bonding mechanism and magnetism in a hexagonal λ1−MgCo2 Laves phase intermetallic formed at rA/rB= 1.280. Ab initio theoretical calculations for MgCo2 using the projector-augmented wave method implemented in the VASP code showed that Mg carries a formal charge +1.7 |e| while Co atoms are also positively charged with around +0.7 |e| being donated to establish the interatomic covalent Co-Co bonding in a three-dimensional network of Co tetrahedra. MgCo2 is a metallic conductor with ferromagnetic properties and TC=303 K. Neutron Powder Diffraction study showed a collinear ordering of the Co moments, their alignment along the c-axis of the hexagonal unit cell with an average moment of 1.51(2) μB/atom Co. Ab initio computational studies indicate that the Co moments reach the experimentally observed value approx.1.5 μB when the unit cell volume exceeds 160 Å3 (average Co-Co distances 2.43 Å).

New Approaches to Robust Inference on Market (Non-)efficiency, Volatility Clustering and Nonlinear Dependence

Abstract We present novel, robust methods for inference on market (non-)efficiency, volatility clustering, and nonlinear dependence in financial return series. In contrast to existing methodology, our proposed methods are robust against nonlinear dynamics and tail-heaviness of returns. Specifically, our methods only rely on return processes being stationary and weakly dependent (mixing) with finite moments of a suitable order. This includes robustness against power-law distributions associated with nonlinear dynamic models such as GARCH and stochastic volatility. The methods are easy to implement and perform well in realistic settings. We revisit a recent study by Baltussen, van Bekkum, and Da (2019, J. Financ. Econ., 132, 26–48) on autocorrelation in major stock indexes. Using our robust methods, we document that the evidence of the presence of negative autocorrelation is weaker, compared with the conclusions of the original study.

The Structure of Terbium in the Ferromagnetic State.

Metals typically crystallize in highly symmetric structures due to their nondirectional and nonsaturated metallic bonds. Here, we report that terbium metal in its ferromagnetic state adopts an unusual low-symmetry orthorhombic structure with a Cmcm space group. A similar structure has been previously observed only in a few actinide metals with bonding 5f electrons at ambient pressure, such as uranium, neptunium, and plutonium, but with different nearest coordination numbers and bond-length variations. The Tb atom occupies the 4c site (0, ∼0.1661, 1/4), building up -[Tb-Tb]- layers stacking along the b-axis. Our first-principles many-body calculations of the crystal field splitting in the correlated Tb 4f-shell demonstrate that the Cmcm structure for ferromagnetic terbium is stabilized by magneto-elastic forces due to a secondary order of quadrupolar moments in the ferromagnetic state. These findings are significant for further understanding of the nature of terbium, including its electron structure, energy bands, phonons, and magnetism.

Worst-case Omega ratio under distribution uncertainty with its application in robust portfolio selection

AbstractOmega ratio, a risk-return performance measure, is defined as the ratio of the expected upside deviation of return to the expected downside deviation of return from a predetermined threshold described by an investor. Motivated by finding a solution protected against sampling errors, in this paper, we focus on the worst-case Omega ratio under distributional uncertainty and its application to robust portfolio selection. The main idea is to deal with optimization problems with all uncertain parameters within an uncertainty set. The uncertainty set of the distribution of returns given characteristic information, including the first two orders of moments and the Wasserstein distance, can handle data problems with uncertainty while making the calculation feasible.

The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions

The article offers a general formulation for the multipolar field expansion of an inclusion. The multipolar moments of arbitrary order for the ellipsoidal inclusion are derived, showing known features of their elastic fields in both the far and near field. Using integer point enumeration theory, the same formulation is extended to all polytopal inclusions, which serve to model faceted inclusions found in, e.g. igneous and metamorphic rocks, particle reinforced composite materials, or as intermetallic precipitates in alloys. A general algorithm for the calculation of the multipolar moments of polytopes of any number of vertices is derived. A number of examples for tetrahedral, cuboidal and dodecahedral inclusions are given. It is shown that the parity of the axial moment function of a polytopal inclusion mirrors the symmetry of the inclusion. This represents the main properties of their elastic fields, including the long- and near-field decay. If the inclusion is symmetric with respect to a given axes, the fields will decay with 1 / r 2 in the far field and 1 / r 4 in the near field. If symmetry along that direction is lost, as is expected in most real inclusions, the decay rate progresses with 1 / r 2 but the near field with 1 / r 3 .

General-relativistic Radiation Transport Scheme in Gmunu. I. Implementation of Two-moment-based Multifrequency Radiative Transfer and Code Tests

We present the implementation of a two-moment-based general-relativistic multigroup radiation transport module in the General-relativistic multigrid numerical (Gmunu) code. On top of solving the general-relativistic magnetohydrodynamics and the Einstein equations with conformally flat approximations, the code solves the evolution equations of the zeroth- and first-order moments of the radiations in the Eulerian-frame. An analytic closure relation is used to obtain the higher order moments and close the system. The finite-volume discretization has been adopted for the radiation moments. The advection in spatial space and frequency-space are handled explicitly. In addition, the radiation–matter interaction terms, which are very stiff in the optically thick region, are solved implicitly. The implicit–explicit Runge–Kutta schemes are adopted for time integration. We test the implementation with a number of numerical benchmarks from frequency-integrated to frequency-dependent cases. Furthermore, we also illustrate the astrophysical applications in hot neutron star and core-collapse supernovae modelings, and compare with other neutrino transport codes.

What is the Fourier Transform of a Spatial Point Process?

This paper determines how to define a discretely implemented Fourier transform when analysing an observed spatial point process. To develop this transform we answer four questions; first what is the natural definition of a Fourier transform, and what are its spectral moments, second we calculate fourth order moments of the Fourier transform using Campbell’s theorem. Third we determine how to implement tapering, an important component for spectral analysis of other stochastic processes. Fourth we answer the question of how to produce an isotropic representation of the Fourier transform of the process. This determines the basic spectral properties of an observed spatial point process.

Characterizing the Spatio-Temporal Variations of Urban Growth with Multifractal Spectra.

Urban morphology exhibits fractal characteristics, which can be described by multifractal scaling. Multifractal parameters under positive moment orders primarily capture information about central areas characterized by relatively stable growth, while those under negative moment orders mainly reflect information about marginal areas that experience more active growth. However, effectively utilizing multifractal spectra to uncover the spatio-temporal variations of urban growth remains a challenge. To addresses this issue, this paper proposes a multifractal measurement by combining theoretical principles and empirical analysis. To capture the difference between growth stability in central areas and growth activity in marginal areas, an index based on generalized correlation dimension Dq is defined. This index takes the growth rate of Dq at extreme negative moment order as the numerator and that at extreme positive moment order as the denominator. During the stable stage of urban growth, the index demonstrates a consistent pattern over time, while during the active stage, the index may exhibit abnormal fluctuations or even jumps. This indicates that the index can reveal spatio-temporal information about urban evolution that cannot be directly observed through multifractal spectra alone. By integrating this index with multifractal spectra, we can more comprehensively characterize the evolutionary characteristics of urban spatial structure.

Structure, chemical reactivity, NBO, MEP analysis and thermodynamic parameters of pentamethyl benzene using DFT study

This study explores the structural, molecular and electronic properties of the pentamethyl benzene (PMB) using quantum chemical calculations employing DFT/ B3LYP/6–311++G(d,p) level of theory. Structural parameters, HOMO-LUMO energies, chemical reactivity descriptors and molecular electrostatic potential (MEP) were evaluated from the optimized molecular geometry. The computed small band gap energy, correlated with the UV–visible spectrum, demonstrates that the test molecule has good biological activity. NLO activity of the molecule was also studied by evaluating dipole moment and first order hyperpolarizability values. Intra-molecular charge transfer, donor-acceptor transitions and stabilizations energies were determined from the analyses of natural bond orbital (NBO) and natural population. 1H and 13C chemical shifts were computed from the simulated NMR spectrum following GIAO approach in DMSO‑d6 solvent at the same level of DFT. Furthermore, thermodynamic parameters and rotational constants were also calculated for this molecule.