Higher-order Moments Research Articles

Higher-order statistical moments of predicted sonic boom waveforms through turbulence

Sonic booms generated by supersonic aircraft are affected by turbulence in the atmospheric boundary layer through which they propagate. Turbulence effects lead to random variability of the sonic boom waveforms measured on the ground, complicating the prediction of such waveforms. As an initial effort to predict the waveform variability, the solution of the coherent or mean sonic boom waveform has previously been formulated by the author. The current paper extends the formulation to derive an expression of the second-order statistical moment necessary to calculate the variance of the spectral amplitudes. Since the derivation uses a full wave equation, results using the derived expression will be compared with those obtained using a parabolic approximation. In order to fully quantify the uncertainty of our predictions, the higher order statistical moments are also formulated and are shown to be approximately zero. Consequently, the probability density function (pdf) of the spectral amplitudes is predicted to be Gaussian. The formulation is further extended to determine the pdf of the loudness of sonic booms and quantify the uncertainties associated with the loudness prediction. Results from the formulation are compared with available flight test data.

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.

Risk Management Effects of Insurance Purchase and Organization Participation: Which Is More Effective?

Insurance purchase and organization participation in risk management is of great practical significance for stabilizing agricultural production and household income. The aims of this study were to analyze farm households’ choices of insurance purchase and organization participation, and their effects on crop revenue and its higher-order moments using the multinomial switching endogenous regression (MESR) model. The results showed that the adoption of insurance and organization was significantly affected by household head characteristics, farm household characteristics, and cropland attributes. Insurance purchase, organization participation, and their joint adoption contributed to the increase in crop revenue and decrease in crop revenue variance, and the benefits were larger when adopting two risk management tools in combination. When skewness was taken into account in risk management analysis, insurance purchase, organization participation, and their joint adoption resulted in a reduction in the probability of crop failure, of which, participating in organizations was the most effective. Efforts should be put forth to improve the functioning and effectiveness of agricultural insurance and organization to promote the adoption of risk management tools.

Texture feature analysis of MRI-ADC images to differentiate glioma grades using machine learning techniques

Apparent diffusion coefficient (ADC) of magnetic resonance imaging (MRI) is an indispensable imaging technique in clinical neuroimaging that quantitatively assesses the diffusivity of water molecules within tissues using diffusion-weighted imaging (DWI). This study focuses on developing a robust machine learning (ML) model to predict the aggressiveness of gliomas according to World Health Organization (WHO) grading by analyzing patients’ demographics, higher-order moments, and grey level co-occurrence matrix (GLCM) texture features of ADC. A population of 722 labeled MRI-ADC brain image slices from 88 human subjects was selected, where gliomas are labeled as glioblastoma multiforme (WHO-IV), high-grade glioma (WHO-III), and low-grade glioma (WHO I-II). Images were acquired using 3T-MR systems and a region of interest (ROI) was delineated manually over tumor areas. Skewness, kurtosis, and statistical texture features of GLCM (mean, variance, energy, entropy, contrast, homogeneity, correlation, prominence, and shade) were calculated using ADC values within ROI. The ANOVA f-test was utilized to select the best features to train an ML model. The data set was split into training (70%) and testing (30%) sets. The train set was fed into several ML algorithms and selected most promising ML algorithm using K-fold cross-validation. The hyper-parameters of the selected algorithm were optimized using random grid search technique. Finally, the performance of the developed model was assessed by calculating accuracy, precision, recall, and F1 values reported for the test set. According to the ANOVA f-test, three attributes; patient gender (1.48), GLCM energy (9.48), and correlation (13.86) that performed minimum scores were excluded from the dataset. Among the tested algorithms, the random forest classifier(0.8772 ± 0.0237) performed the highest mean-cross-validation score and selected to build the ML model which was able to predict tumor categories with an accuracy of 88.14% over the test set. The study concludes that the developed ML model using the above features except for patient gender, GLCM energy, and correlation, has high prediction accuracy in glioma grading. Therefore, the outcomes of this study enable to development of advanced tumor classification applications that assist in the decision-making process in a real-time clinical environment.

A novel decomposition-based approach for non-stationary hub-height wind speed modelling

An accurate description of hub-height wind speed characteristics is indispensable to offshore wind resource assessment and structure reliability analysis. However, given the assumption of stationarity in wind speeds that is violated, the commonly used stationary statistical models will lead to bias, and a non-stationary frequency analysis is required. In this paper, a novel decomposition-based non-stationary modelling approach was proposed. To decompose time series into deterministic and stochastic components, a procedure was designed by combining signal decomposition methods and recurrence quantification analysis and the performances of seven signal decomposition methods were evaluated under various represent non-stationary scenarios via numerical experiments. Then the non-stationary model was established by aggregating the modelled two components. Compared with other methods, the proposed approach is superior, which is of good self-adaption to data and relies on no hypotheses and explanatory covariates, guaranteeing the simplicity and reliability of the constructed models. Additionally, the SSA-based procedure is capable of capturing complicated non-stationary patterns while preserving the higher-order moments of the underlying stochastic process. The capacity of the proposed approach was verified using wind speed data at six positions distributed along China's coastline. Results emphasize the importance of the consideration of non-stationarity and the necessity of this study.

Spillovers of joint volatility-skewness-kurtosis of major cryptocurrencies and their determinants

Spillovers in high-order moments are understudied in the cryptocurrency markets, and notably their joint volatility-skewness-kurtosis spillover effect and its drivers are overlooked. In this paper, we examine dynamics of the spillovers of joint volatility-skewness-kurtosis of major cryptocurrencies and reveal the macroeconomic, financial, and geopolitical factors driving these spillovers. Methodologically, we first use the autoregressive conditional density model to extract the daily higher-order conditional moments of major cryptocurrencies (Bitcoin, Ethereum, Ripple, Litecoin, and Monero) from 9th August 2015 to 23rd September 2021, and then apply the spillover approach to the extracted conditional higher-order moments, namely conditional volatility, conditional skewness, and conditional (excess) kurtosis, in static and dynamic settings. The results show the following: Firstly, cryptocurrencies are interlinked in a time-varying manner by their conditional volatility, conditional skewness, and conditional (excess) kurtosis. Secondly, the spillover index estimated jointly for these three conditional moments exceeds the sum of the three spillover indices estimated for each conditional moment separately, confirming the existence of interdependence across the three conditional moments. Thirdly, inflation expectation, precious metals volatility, and trading volume are significant determinants of the joint volatility-skewness-kurtosis spillover index, irrespective of the pandemic; the investors' focal point switches from the significant corporate spreads before the COVID-19 outbreak to the vital role the term spread plays during the COVID-19 era as a leading indicator of the economic cycle and growth prospect. Financial stress and geopolitical risk are also important, as indicated by the causality-in-quantile analysis. These findings are relevant to investment decisions and policy formulation.

Scaling of whole-brain dynamics reproduced by high-order moments of turbulence indicators

Scaling of whole-brain dynamics reproduced by high-order moments of turbulence indicators

Adaptive robust large volatility matrix estimation based on high-frequency financial data

Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order moment assumption for observed log-returns, which cannot account for the heavy-tail phenomenon of stock-returns. Recently, a robust estimator was developed to handle heavy-tailed distributions with some bounded fourth-moment assumption. However, we often observe that log-returns have heavier tail distribution than the finite fourth-moment and that the degrees of heaviness of tails are heterogeneous across asset and over time. In this paper, to deal with the heterogeneous heavy-tailed distributions, we develop an adaptive robust integrated volatility estimator that employs pre-averaging and truncation schemes based on jump-diffusion processes. We call this an adaptive robust pre-averaging realized volatility (ARP) estimator. We show that the ARP estimator has a sub-Weibull tail concentration with only finite 2α-th moments for any α>1. In addition, we establish matching upper and lower bounds to show that the ARP estimation procedure is optimal. To estimate large integrated volatility matrices using the approximate factor model, the ARP estimator is further regularized using the principal orthogonal complement thresholding (POET) method. The numerical study is conducted to check the finite sample performance of the ARP estimator.

Transport of Spin Magnetic Multipole Moments Carried by Bloch Quasiparticles.

Magnetic ordering beyond the standard dipolar order has attracted significant attention in recent years, but it remains an open question how to effectively manipulate such nontrivial order parameters using external perturbations such as electric currents or fields. In particular, it is desirable to have a conceptual tool similar to nonequilibrium spin currents in spintronics to describe the creation and transport of multipole moments. In this context, we present a theory for Cartesian spin magnetic multipole moments of Bloch quasiparticles and their transport based on a general gauge-invariant formula obtained using the wave packet approach. As a concrete example, we point out that the low-energy Hamiltonian of phosphorene subject to a perpendicular electric field has a valley structure that hosts magnetic octupole moments. The magnetic octupole moments can be exhibited by an in-plane electric current and lead to accumulation of staggered spin densities at the corners of a rectangular sample. Our Letter paves the way for systematically seeking and utilizing quasiparticles with higher-order magnetic multipole moments in crystal materials towards the emergence of multipoletronics.

Strategies for Computational Fluid Dynamics Validation Experiments

Abstract The Benchmark Validation Experiment for Reynolds-averaged Navier–Stokes (RANS)/large eddy simulation (LES) Investigations (BeVERLI) aims to produce an experimental dataset of three-dimensional non-equilibrium turbulent boundary layers with various levels of separation that, for the first time, meets the most exacting requirements of computational fluid dynamics validation. The application of simulations and modeling in high-consequence engineering environments has become increasingly prominent in the past two decades, considerably raising the standards and demands of model validation and forcing a significant paradigm shift in the design of corresponding validation experiments. In this paper, based on the experiences of project BeVERLI, we present strategies for designing and executing validation experiments, hoping to ease the transition into this new era of fluid dynamics experimentation and help upcoming validation experiments succeed. We discuss the selection of a flow for validation, the synergistic use of simulations and experiments, cross-institutional collaborations, and tools, such as model scans, time-dependent measurements, and repeated and redundant measurements. The proposed strategies are shown to successfully mitigate risks and enable the methodical identification, measurement, uncertainty quantification, and characterization of critical flow features, boundary conditions, and corresponding sensitivities, promoting the highest levels of model validation experiment completeness per Oberkampf and Smith [1]. Furthermore, the applicability of these strategies to estimating critical and difficult-to-obtain bias error uncertainties of different measurement systems, e.g., the underprediction of high-order statistical moments from particle image velocimetry velocity field data due to spatial filtering effects, and to systematically assessing the quality of uncertainty estimates is shown.

The role of higher moments in predicting China's oil futures volatility: Evidence from machine learning models

This paper expands the emerging literature on volatility forecasting for China's oil market by exploring the predictive ability of higher-order moments (skewness, kurtosis, hyperskewness, and hyperkurtosis) based on high-frequency data. Our investigation is originally based on the heterogeneous autoregressive (HAR) framework, but considering the possible multicollinearity and nonlinearity, it is extended to various machine learning (ML) models and combination forecasting models. The results reveal that higher-order moments, including the two highest moments, always significantly improve predictive performance for the COVID-19 crisis. We further examine the interpretability of ML models and each factor's contribution to the prediction, finding that odd and even moments contain short- and long-term prediction information, respectively. This paper also highlights the effectiveness of ML models for capturing trends in oil futures volatility with higher-order moments and the satisfactory performance of combination forecasting models. Finally, we investigate the predictability of asymmetric risk patterns and obtain identical results. Our study has important implications for financial risk management, asset pricing, and portfolio allocation.

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.

Random walks on modular chains: Detecting structure through statistics.

We study kinetic transport through one-dimensional modular networks consisting of alternating domains using both analytical and numerical methods. We demonstrate that the mean velocity is insensitive to the local structure of the network, and it depends only on global, structural-averaged properties. However, by examining high-order cumulants characterizing the kinetics, we reveal information on the degree of inhomogeneity of blocks and the size of repeating units in the network. Specifically, in unbiased diffusion, the kurtosis is the first transport coefficient that exposes structural information, whereas in biased chains, the diffusion coefficient already reveals structural motifs. Nevertheless, this latter dependence is weak, and it disappears at both low and high biasing. Our study demonstrates that high-order moments of the population distribution over sites provide information about the network structure that is not captured by the first moment (mean velocity) alone. These results are useful towards deciphering mechanisms and determining architectures underlying long-range charge transport in biomolecules and biological and chemical reaction networks.

Higher-order moment nexus between the US Dollar, crude oil, gold, and bitcoin

This paper explores the relationships between the US dollar, crude oil, gold, and bitcoin by taking into account the higher-moment linkages. Specifically, we construct robust estimators for the realized volatility, realized skewness, realized kurtosis, and jump, and study the causalities between the estimators through the Granger causality test. A generalized impulse response analysis identified by our quad-variate VAR specification is further implemented to uncover the lead-lag spillover effect across the variables of interest. We utilize high-frequency data for the chosen assets from January 3, 2016, to June 23, 2022, and observe various patterns of cross-market interconnection related to higher-order moments. These findings suggest that systematic risk factors must be considered while jointly modeling market linkages. Practical implications for investors and market regulators are also discussed.

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.

Fast and accurate computation of polar harmonic Fourier moments for image description.

Continuous orthogonal moments are widely used in various image techniques due to their simplicity and good rotational invariance and stability. In recent years, numerous excellent continuous orthogonal moments have been developed, among which polar harmonic Fourier moments (PHFMs) exhibit strong image description capabilities. However, the numerical integration error is large in the calculation, which seriously affects the calculation accuracy, especially in higher-order calculation. In this paper, a continuous orthogonal moments-fast and accurate PHFM (FAPHFM) is proposed. It utilizes the polar pixel tiling technique to reduce numerical errors in the computation; this method particularly improves the accuracy of higher-order moments of traditional PHFMs. However, as accuracy increases, calculation complexity also increases. To address this issue, an eight-way symmetric/anti-symmetric calculation of the angular and radial functions was performed using the symmetry and anti-symmetry of traditional PHFMs, and clustering of pixels was performed as a way to improve the computational speed. The experimental results show that FAPHFMs perform better in image reconstruction (including noise), with higher computational accuracy, lower time complexity, and better image description ability.

The practical calculation method of the high-order moment spectra of quadratic Gaussian stochastic processes

In the frequency-domain analysis of structures under non-Gaussian excitations, the determination of high-order moment spectra of excitations remains a substantial challenge due to the complexity and inaccuracy of the existing estimation method. This paper proposes the practical calculation method of the high-order moment spectra models for quadratic Gaussian stochastic processes. Firstly, the expressions of the first four moment spectra of quadratic Gaussian stochastic processes are derived based on the relation between the high-order cumulant function of Gaussian stochastic processes and high-order moment function. Secondly, a practical calculation method of the high-order moment spectra is presented by the ratio of the corresponding component moment functions. Finally, two numerical examples are investigated to validate the efficiency and accuracy of the practical calculation method of the high-order moment spectra for quadratic Gaussian stochastic processes.

Classification of Epileptic and Psychogenic Nonepileptic Seizures via Time-Frequency Features of EEG Data.

The majority of psychogenic nonepileptic seizures (PNESs) are brought on by psychogenic causes, but because their symptoms resemble those of epilepsy, they are frequently misdiagnosed. Although EEG signals are normal in PNES cases, electroencephalography (EEG) recordings alone are not sufficient to identify the illness. Hence, accurate diagnosis and effective treatment depend on long-term video EEG data and a complete patient history. Video EEG setup, however, is more expensive than using standard EEG equipment. To distinguish PNES signals from conventional epileptic seizure (ES) signals, it is crucial to develop methods solely based on EEG recordings. The proposed study presents a technique utilizing short-term EEG data for the classification of inter-PNES, PNES, and ES segments using time-frequency methods such as the Continuous Wavelet transform (CWT), Short-Time Fourier transform (STFT), CWT-based synchrosqueezed transform (WSST), and STFT-based SST (FSST), which provide high-resolution time-frequency representations (TFRs). TFRs of EEG segments are utilized to generate 13 joint TF (J-TF)-based features, four gray-level co-occurrence matrix (GLCM)-based features, and 16 higher-order joint TF moment (HOJ-Mom)-based features. These features are then employed in the classification procedure. Both three-class (inter-PNES versus PNES versus ES: ACC: 80.9%, SEN: 81.8%, and PRE: 84.7%) and two-class (Inter-PNES versus PNES: ACC: 88.2%, SEN: 87.2%, and PRE: 86.1%; PNES versus ES: ACC: 98.5%, SEN: 99.3%, and PRE: 98.9%) classification algorithms performed well, according to the experimental results. The STFT and FSST strategies surpass the CWT and WSST strategies in terms of classification accuracy, sensitivity, and precision. Moreover, the J-TF-based feature sets often perform better than the other two.

Variance reduced particle solution of the Fokker-Planck equation with application to rarefied gas and plasma dynamics

We develop an importance-weight-based variance reduction method for direct Monte Carlo simulations of the Fokker-Planck equation with applications to rarefied gas and plasma dynamics. We show that there exists a class of Fokker-Planck equations that admit stable weight evolution processes along particle trajectories, including those with drift and diffusion coefficients independent of moments higher than the kinetic energy, such as the linearized Landau equation. When drift or diffusion coefficients depend on higher-order moments, such as in the cubic Fokker-Planck equation, maintaining stability and accuracy of the weight evolution becomes challenging. In this work, stability and conservation for the cubic FP model are achieved using the maximum cross-entropy formulation introduced in recent work Sadr and Hadjiconstantinou (2023) [30]. Several test cases show that significant speed-up is obtained using the proposed variance reduced method compared to the standard Monte Carlo solution in the low-signal limit.

Multivariate dynamics between emerging markets and digital asset markets: An application of the SNP-DCC model

As crypto markets become more integrated, measuring their spillovers with financial markets becomes fundamental for portfolio choice and risk management. We investigate high-order moment transmission between emerging/developed and digital asset markets through a flexible semi-nonparametric approach that accounts for dynamic conditional correlation and spillover effects, not only in conditional volatility but also in conditional skewness and kurtosis. The results show a (positive) transmission of volatility from emerging and developed markets to digital asset markets, as a signal of market integration, but also some positive/negative skewness and kurtosis spillovers (remarkably from Crypto and Blockchain indices to Emerging Asia and Latin America indices) detected at daily and weekly basis.