Higher-order Moments Research Articles

The dynamic risk spillover of higher-order moments in the China’s energy market: A time-frequency perspective

ABSTRACT This study employs a risk spillover measurement method based on CEEMDAN-SE, GARCHSK, and TVP-VAR-DY models to assess risk spillover among 11 sub-sectors in China’s energy market, such as coal, oil, thermal power, and new energy vehicles. The energy sector index return is decomposed into intrinsic mode functions (IMFs) and reconstructed into high, medium, and low-frequency sequences. The GARCHSK model calculates conditional mean, variances, skewness, and kurtosis sequences for these sequences, which are then integrated into the TVP-VAR-DY model to evaluate return, volatility, and higher-order moment risk spillovers. Empirical findings highlight significant time-varying spillover effects, with return and volatility spillovers surpassing average total skewness and kurtosis spillovers. The New Energy Vehicle (NEV) and Electric Power Grid (EPG) sectors act as major risk transmitters, while primary risk receivers vary by frequency and order. Regulatory authorities should develop a real-time surveillance mechanism to monitor the transfer of risks between the NEV sector and the EPG sector. It is essential to foster inter-industry cooperation to facilitate better resource allocation and swift response to emerging challenges. Furthermore, policymakers should focus on bolstering the resilience of pivotal sectors by employing dynamic risk management strategies and providing appropriate incentives.

The asymmetric response of higher-order moments of precious metals to energy shocks and financial stresses: Evidence from time-frequency connectedness approach

The asymmetric response of higher-order moments of precious metals to energy shocks and financial stresses: Evidence from time-frequency connectedness approach

Bivariate density estimation under marginal unimodality constraints

Empirical analyses of observed pairs of variables often suggest that the underlying joint distribution of these variables is highly dependent and each one of them is marginally unimodal. Exploiting marginal shape information can improve the bivariate density estimation. We develop a nonparametric density estimation method where the joint density of the bivariate outcome variables is estimated using a flexible class of mixtures of scaled Beta distributions and the mixing weights are suitably constrained to ensure marginal unimodality. Large sample consistency of the proposed density estimator is established using the method of sieves and Argmax Continuous Mapping Theorem. The proposed method enlarges the scope of previous studies in two important aspects: (i) joint density provides a simultaneous estimation of higher-order moments beyond mean and variance functions, and (ii) marginal shape constraints provide more efficient estimates. The proposed procedures are illustrated using simulated and real case study datasets on gestational age and infant birth weight.

The Impact of Sentiment on Realized Higher-Order Moments in the S&P 500: Evidence from the Fear and Greed Index

This study empirically investigates the relationship between realized higher-order moments and the Fear and Greed Index as a measure of sentiments. We estimate daily realized moments using 5 min return data of the S&P 500 index from 3 January 2011 to 18 September 2020. We find that the Fear and Greed Index significantly impacts realized volatility during periods of extreme fear. Additionally, various sentiment indicators influence realized skewness and realized kurtosis. The VIX index significantly reduces realized skewness across all sentiment levels. Bearish and bullish sentiments have a significant negative relationship with negative realized skewness during periods of extreme fear and extreme greed. However, the Fear and Greed Index and bearish and bullish sentiments have a significant positive relationship with positive realized skewness. During extreme fear, the Fear and Greed Index and bearish and bullish sentiments have a significant negative relationship with realized kurtosis. These results remain consistent when considering the non-linear characteristics of the Fear and Greed Index during periods of extreme fear and extreme greed. These findings highlight the relevance of understanding sentiment in financial risk management and its significant relationship with the asymmetric and extremity characteristics of asset returns.

Exact Moments of Residuals of Independence

The diagnosis of residuals of independence is critical in association analysis and loglinear modeling of two-way contingency tables. Most residual diagnostics depend on large-sample methods, and diagnostic results become dubious when sample sizes are small or data are sparse. In such cases, statistical inference based on non-asymptotic theory or exact inference is desirable. This paper explicitly derives the first four moments of the residuals of independence in a two-way contingency table under a multinomial model. These exact moments are necessary tools for studying the analytical features of the distribution of residuals of independence, such as skewness and kurtosis. Higher-order moments can be found similarly, but the results are more complicated.

Higher-Order Moment Risk and ESG Sentiment: Evidence from China’s Options Market

The relationship between risk and return is an important topic in financial research. In this paper, we investigate the factors affecting the higher-order moment risk premiums. The results indicate that there is a significant interaction between variance, skewness and kurtosis when considering risk premiums. This implies that there are both common and independent sources of risk information. In addition, ESG news sentiment has a significant positive effect on volatility risk premium.

High order moment conserving method of classes in CFD code

Abstract Dispersed multiphase flows are widely present in the majority of chemical process industry equipment. For the purpose of design, optimization, and scale up of these industrial systems, robust, accurate and fast simulation methods are needed, especially when coupling computational fluid dynamics (CFD) with population balance models (PBM). In this work, the high-order moment conserving method of classes (HMMC) is implemented and tested within the commercial CFD software of ANSYS Fluent with two simple well-defined test cases and a realistic 3D simulation of rotating disc (RDC) extractor. Firstly, a zero-dimensional PBM with well-mixed assumption and no convection was solved for a single computational cell in Fluent to verify the implementation in comparison with a simple reactor model in MATLAB. Secondly, the convection was considered by solving a one-dimensional PBM for three computational cells side by side in Fluent and compared with an equivalent three staged reactor model in MATLAB. Eventually, realistic 3D RDC simulations were conducted to fully couple the HMMC and CFD in Fluent. The implementation of HMMC was compared to predictions with other state-of-the-art PBM solution methods, e.g., the quadrature method of moments (QMOM) and the fixed pivot technique (FPT) in Fluent and MATLAB platforms. The implementation of the HMMC in Fluent platform was straightforward with no additional challenges. The verification shows that the HMMC approach is robust and efficient for polydispersed multiphase CFD simulations.

Vlasov simulations of electric propulsion beam

Abstract A grid-based Vlasov simulation model is developed to simulate the two-dimensional unmagnetized electric propulsion (EP) plasma beam emission process. Comparing to the standard fully kinetic Particle-in-Cell simulation, the grid-based Vlasov simulation method eliminates the interference of particle noise and is capable of resolving higher-order velocity moment, such as electron heat flux, accurately. Vlasov simulations are carried out to investigate the effects of microscopic electron kinetics on macroscopic electron thermodynamics in EP beam. We find that the electron velocity distribution function (eVDF) exhibits a near-Maxwellian shape but with a depleted negative velocity tail in the beam direction and a ‘top-hat’ shape in the transverse direction. Macroscopically, the electrons confined within the quasi-neutral beam core region has a near constant temperature along the beam direction but follow a near-adiabatic cooling process as they expand outward in the transverse direction. The electron heat flux is dominated by the x-direction tensor component. The connection between the eVDF skewness and the electron heat flux suggests a pathway to develop a microscopic physics based electron closure relation for macroscopic electron thermodynamic process in unmagnetized plasma beam expansion.

Experimental investigation of the flow disturbance near the trailing edge of slotted and non-slotted blades using skewness and kurtosis

ABSTRACT The present study conducts an experimental investigation into the flow characteristics over a cascade of both slotted and non-slotted compressor blades. The focus is on evaluating potential statistical correlations between higher-order moments of velocity fluctuations, including Skewness and Kurtosis. The linear axial cascade comprises three NACA6409 blades, which are tested in both normal and slotted blade. Data acquisition was conducted using a hot wire anemometer at three measurement stations within the cascade. The hot wire sensor was positioned at distances of x/c = 0.125, 0.25, and 0.5 from the trailing edge (x), where x represents the distance from the probe to the trailing edge of the airfoil and (c) is the chord length of the blade. Measurements were taken at a blade angle of attack of 0° and two Reynolds numbers: 22,750 and 45,500. Results indicate that blade grooving enhances flow velocity, postpones separation and improves flow control in the trailing edge region. By comparing calculated Skewness and Kurtosis values with those predicted by existing boundary layer and free jet relations, more consistent correlations were identified. To provide more accurate relationships, two polynomials of the second and third order have been used. It was found that high-order values of velocity were obtained more accurately with the relations presented in this research. Although the accuracy of these predictions is significantly reduced in the proportion of larger distances. In distant stations, the loss velocity has decreased. As the distance from the model increases, the amount of inhomogeneities in the sequence increases and the values of the opposite Skewness become zero. Turbulence intensity has been reduced by slotting the blades.

Demand Risks and Term Structure of Volatility Index Futures

In this paper, we develop an equilibrium framework to explain the characteristics of volatility index (VIX) futures prices and returns across maturities. In the framework, the investors prefer VIX futures with specific maturities, and the arbitrageurs optimize portfolios based on mean-variance preferences. The model-implied futures prices are affected by the variance and demand risk factors. Theoretical and empirical analyses show that incorporating jump risks helps to explain the higher-order moments of futures and that including the demand factor improves futures pricing performance.

Improving the estimate of higher-order moments from lidar observations near the top of the convective boundary layer

Abstract. Ground-based lidar data have proven extremely useful for profiling the convective boundary layer (CBL). Many groups have derived higher-order moments (e.g., variance, skewness, fluxes) from high-temporal-resolution lidar data using an autocovariance approach. However, these analyses are highly uncertain near the CBL top when the depth of the CBL (zi) is changing during the analysis period. This is because the autocovariance approach is usually applied to constant height levels and the character of the eddies is changing on either side of the changing CBL top. Here, a new approach is presented wherein the autocovariance analysis is performed on a normalized height grid, with a temporally smoothed zi. Output from a large eddy simulation model demonstrates that deriving higher-order moments from time series on a normalized height grid has better agreement with the slab-averaged quantities than the moments derived from the original height grid.

A study of gust wind speed using a novel unsteady Reynolds-Averaged Navier-Stokes model

In this study, a novel unsteady Reynolds-Averaged Navier-Stokes (URANS) model is proposed in conjunction with a prespecified averaging time and turbulent inflow, and a new peak factor that considers the effect of averaging time used in URANS is derived to calculate gust wind speed. Firstly, the URANS incorporated with a prespecified averaging time and turbulent inflow is proposed to predict the time series of wind speed over flat terrain and investigate the variation of higher-order moments and zero-crossing rate at which the fluctuating wind speed changes algebraic sign with the averaging time. The predicted higher-order moments are less sensitive to the averaging time, but the predicted zero-crossing rate slightly decrease with increasing the averaging time due to the moving average effect. Secondly, a new peak factor is proposed to consider the averaging time. Finally, the gust wind speeds over flat terrain and around a single building predicted using the proposed URANS and the new peak factor based on the Hermite model are found to be in good agreement with the LES results, while those predicted by the conventional models deviate more from the LES results.

Higher-order moments spillovers among energy, carbon and tourism markets: Time- and frequency-domain evidence.

This paper uses the GJRSK model to estimate the high-order moments of energy (oil, natural gas, and coal), the carbon market, and tourism stocks. Then, it utilizes a novel TVP-VAR time-frequency connectedness approach to examine higher-order moments spillovers among them. The results show a strong connectedness among the three markets. The energy market is the emitter of volatility, skewness and kurtosis spillovers; tourism stock is the receiver; and the carbon market is the transmitter. From a time-domain perspective, the higher-order moments spillovers of the three markets are time-varying, especially during extreme periods, where the energy market's spillover effects on tourism stocks are significantly enhanced, indicating that tourism stocks bear a greater risk at leptokurtosis and fat-tail moment. From a frequency-domain perspective, the long-term asymmetric spillovers of oil, natural gas, and tourism markets on the carbon market are more pronounced than the short-term. Moreover, the COVID-19 pandemic exacerbated the higher-moment spillovers of energy and tourism stocks on the carbon market. Meanwhile, the Russia-Ukraine conflict led to extreme risk transmission within the energy market. These findings have significant implications for cross-industry investors and green finance risk management.

Uniform inference in linear error-in-variables models: Divide-and-conquer

. It is customary to estimate error-in-variables models using higher-order moments of observables. This moments-based estimator is consistent only when the coefficient of the latent regressor is assumed to be nonzero. We develop a new estimator based on the divide-and-conquer principle that is consistent for any value of the coefficient of the latent regressor. In an application on the relation between investment, (mismeasured) Tobin’s q and cash flow, we find time periods in which the effect of Tobin’s q is not statistically different from zero. The implausibly large higher-order moment estimates in these periods disappear when using the proposed estimator.

Closure equationand higher-order moment relations in the Gauss-Hermite lattice Boltzmann method.

Moment methods are often used to solve transport problems involving the Boltzmann-BGK equation. Because the moment equationsare underdetermined, these methods require an additional "closure equation" that relates higher to lower-order moments. Here, we examine the closure equationand higher-order moment relations implicit in the lattice Boltzmann method (LBM) that use Gauss-Hermite quadrature for their discrete velocity sets. It is shown that the discrete-velocity-set itself defines the closure equationand higher-order moment relations, the precise forms of which are yet to be reported. The general formula we present facilitates the efficient computational evaluation of higher-order moments and provides insight into the operation of LBM that is anticipated to be useful in theoretical analyses of its performance. Derived formulas for two different velocity sets are validated against numerical implementations of the LBM for steady Couette flow.

Electron Influence on the Parallel Proton Firehose Instability in 10-moment, Multifluid Simulations

Instabilities driven by pressure anisotropy play a critical role in modulating the energy transfer in space and astrophysical plasmas. For the first time, we simulate the evolution and saturation of the parallel proton firehose instability using a multifluid model without adding artificial viscosity. These simulations are performed using a 10-moment, multifluid model with local and gradient relaxation heat-flux closures in high-β proton–electron plasmas. When these higher-order moments are included and pressure anisotropy is permitted to develop in all species, we find that the electrons have a significant impact on the saturation of the parallel proton firehose instability, modulating the proton pressure anisotropy as the instability saturates. Even for lower β's more relevant to heliospheric plasmas, we observe a pronounced electron energization in simulations using the gradient relaxation closure. Our results indicate that resolving the electron pressure anisotropy is important to correctly describe the behavior of multispecies plasma systems.

The VIRUS-dE Survey. I. Stars in Dwarf Elliptical Galaxies—3D Dynamics and Radially Resolved Stellar Initial Mass Functions

We analyze the stellar structure of a sample of dwarf ellipticals (dEs) inhabiting various environments within the Virgo cluster. Integral-field observations with a high spectral resolution allow us to robustly determine their low-velocity dispersions (∼25 km s−1) and higher-order kinematic moments out to the half-light radius. We find the dEs exhibit a diversity in ages, with the younger dEs being less enhanced than the older, suggesting a complex star formation history for those dEs that recently entered Virgo, while others have been quenched shortly after reionization. Orbit-superposition modeling allowed us to recover viewing angles, stellar mass-to-light ratios (with gradients), as well as the intrinsic orbit structure. We find that the angular momentum of the dEs is strongly suppressed compared to ordinary early-type galaxies and correlates with the environment. Flattened dEs are so because of a suppressed kinetic energy perpendicular to their equatorial plane. Combining population and dynamical modeling results, we find an age-dependent stellar initial mass function or, alternatively, evidence for a more extended star formation history for those galaxies that have had higher initial mass and/or inhabited lower-density environments. dEs appear to have a spatially homogeneous stellar structure, but the state they were “frozen” in as they stopped forming stars varies dramatically according to their initial conditions.

Revisiting each fracture size and spatial pattern: Inference from rock mass surface to interior

Estimating fracture size is a fundamental aspect of rock engineering. However, determining the most probable diameter (MPD) from a fracture’s surface trace remains challenging in the scientific community. The prevailing methodologies typically infer statistical distributions of fracture sizes rather than specific values. This research presents a novel approach to inferring the MPD and the true spatial distribution pattern of each fracture. The challenge lies in linking the inference process with the trace length of each fracture and the statistical characteristics of the entire outcrop. Additionally, it is necessary to address the non-unique inverse problem. The methodology comprises several key steps. Firstly, the issue of censoring bias is addressed by considering the lengths of the traces contained. Secondly, the orientation bias is corrected using the vector method, and the true mean trace length and standard deviation are estimated and derived. Thirdly, assuming a lognormal distribution for fracture sizes, the mean and standard deviation of diameters are derived through a high-order moment relationship between trace lengths and diameters, validated by Crofton’s theorem. Finally, the MPDs of all trace samples are determined by relating MPDs to trace lengths and the standard deviation of diameters using stereology techniques. Furthermore, the true fracture spatial patterns are inverted based on spatial geometric relationships. The proposed methodology is validated through rigorous Monte Carlo simulation and applied in a practical engineering case study, demonstrating its potential for use in rock engineering applications.

Diffusion and Spectroscopy of H2 in Myoglobin

The diffusional dynamics and vibrational spectroscopy of molecular hydrogen (H2) in myoglobin (Mb) is characterized. Hydrogen has been implicated in a number of physiologically relevant processes, including cellular aging or inflammation. Here, the internal diffusion through the protein matrix was characterized, and the vibrational spectroscopy was investigated using conventional empirical energy functions and improved models able to describe higher-order electrostatic moments of the ligand. Depending on the energy function used, H2 can occupy the same internal defects as already found for Xe or CO (Xe1 to Xe4 and B-state). Furthermore, four additional sites were found, some of which had been discovered in earlier simulation studies. Simulations using a model based on a Morse oscillator and distributed charges to correctly describe the molecular quadrupole moment of H2 indicate that the vibrational spectroscopy of the ligand depends on the docking site it occupies. This is consistent with the findings for CO in Mb from experiments and simulations. For H2, the maxima of the absorption spectra cover ∼20 cm−1 which are indicative of a pronounced Stark effect of the surrounding protein matrix on the vibrational spectroscopy of the ligand. Electronic structure calculations show that H2 forms a stable complex with the heme iron (stabilized by ∼−12 kcal/mol), but splitting of H2 is unlikely due to a high activation energy (∼50 kcal/mol).

Quantitative estimation of optical properties in bilayer media within the subdiffusive regime using a tilted fiber-optic probe in diffuse reflectance spectroscopy, part 1: a theoretical framework for designing probe geometry.

As biological tissues are highly heterogeneous, there is a great interest in developing non-invasive optical approaches capable of characterizing them in a very localized manner. Obtaining accurate absolute values of the local optical properties from the measured reflectance requires finding a probe geometry, which allows us to solve this inverse problem robustly and reliably despite neglecting the higher-order moments of the scattering phase function. Our goal is to develop a theoretical framework for designing tilted-fiber diffuse reflectance probes that allow quantitative estimation of the optical properties corresponding to limited tissue volume (typically a few cubic millimeters). Relationships among probe geometry, sampled tissue volume, and robustness of the inverse solver to calculate optical properties from reflectance are studied using Monte Carlo simulations. The analysis of the number of scattering events of the collected photons leads to the establishment of relationships among the probe geometry, the sampled tissue volume, and the validity of a subdiffusive regime for the reflectance. A methodology is proposed for the design of new compact probes with tilted fiber geometry that can quantitatively estimate the values of the optical coefficients in a localized manner within living biological tissues by recording diffuse reflectance spectra.