Higher-order Moments Research Articles

Higher-order moments of the Mott-Smith shock approximation

Higher-order moments of the Mott-Smith shock approximation

Multivariate copula-based conditional quantiles: analytic higher-order moments and ratio estimation approaches

ABSTRACT In this paper, we aim to modify multivariate copula-based conditional quantiles for a targeted random variable, given multiple random variables attaining their respective quantiles. Specifically, we propose two modifications through the Cornish–Fisher expansion, one of which involves its analytic higher-order unconditional moments. The second one accounts for its higher-order conditional moments estimated using a ratio estimation method. By considering multivariate elliptical and Archimedean copulas with Johnson's SU margins, our simulation study shows that this method provides more accurate conditional moment estimators compared to the naive method. They result in expanded conditional quantile estimators, whose efficiency is relatively better than their unexpanded versions, particularly at lower and higher quantile levels under a stronger (tail) dependence assumption. A much higher efficiency is gained when the first modification is performed. These findings are validated using an empirical study based on cryptocurrency return data and a comparative analysis against the existing estimation approaches.

Information Theoretic Evaluation of Raccoon's Side-Channel Leakage

Raccoon is a lattice-based scheme submitted to the NIST 2022 call for additional post-quantum signatures. One of its main selling points is that its design is intrinsically easy to mask against side-channel attacks. So far, Raccoon's physical security guarantees were only stated in the abstract probing model. In this paper, we discuss how these probing security results translate into guarantees in more realistic leakage models. We also highlight that this translation differs from what is usually observed (e.g., in symmetric cryptography), due to the algebraic structure of Raccoon's operations. For this purpose, we perform an in-depth information theoretic evaluation of Raccoon's most innovative part, namely the AddRepNoise function which allows generating its arithmetic shares on-the-fly. Our results are twofold. First, we show that the resulting shares do not enforce a statistical security order (i.e., the need for the side-channel adversary to estimate higher-order moments of the leakage distribution), as usually expected when masking. Second, we observe that the first-order leakage on the (large) random coefficients manipulated by Raccoon cannot be efficiently turned into leakage on the (smaller) coefficients of its long-term secret. Concretely, our information theoretic evaluations for relevant leakage functions also suggest that Raccoon's masked implementations can ensure high security with less shares than suggested by a conservative analysis in the probing model.

Analysis of the Gaussian assumption of single sound source measured and processed through sound level meter

Machine learning (ML) techniques are constantly growing in acoustics. Such methods exploit large databases to train algorithms and earn complex feature correlations. The primary goal is to obtain inferences and predictions. Thus, ML often exploits statistics, and understanding the data distribution becomes fundamental when analyzing the available data. However, it is well-known that only some common methods can be used with large databases, e.g., normality tests are discouraged. The present work aims to explore the Gaussian assumption underlying a validated clustering technique used in long-term monitoring of sound level meters. The Gaussianity of single sound sources is analyzed through normal tests, normal probability plots, cumulative distribution functions, and high-order moments. The analysis involves a real-world measurement carried out through a sound level meter and speech recordings obtained from a common database used in machine learning. Results show that a single sound source can be deemed Gaussian in sound level meter long-term measurements, leading to important insights concerning the choice of algorithms.

The Lower Limit of Dynamical Black Hole Masses Detectable in Virgo Compact Stellar Systems Using the JWST/NIRSpec IFU

Due to observational challenges, the mass function of black holes (BH) at lower masses is poorly constrained in the local universe. Understanding the occupation fraction of BHs in low-mass galaxies is crucial for constraining the origins of supermassive BH seeds. Compact stellar systems (CSSs), including ultracompact dwarf galaxies (UCDs) and compact elliptical galaxies (cEs), are potential intermediate-mass BH hosts. Despite the difficulties posed by their limited spheres of influence, stellar dynamical modeling has been effective in estimating central BH masses in CSSs. Some CSSs may harbor a BH constituting up to 20% of their host stellar mass, while others might not have a central BH. In support of our ongoing efforts to determine the BH masses in select CSSs in the Virgo cluster using JWST/NIRSpec IFU observations and orbit-superposition dynamical models, we create mock kinematic data mimicking the characteristics of observed cEs/UCDs in the Virgo cluster with different BH masses. We then construct a series of dynamical models using the orbit-superposition code FORSTAND and explore the accuracy of recovering the BH mass. We find that the mass of BHs comprising 1% or more of the total host stellar mass can be accurately determined through kinematic maps featuring higher-order velocity moments. We also assess how BH mass measurement is affected by deprojection methods, regularization factors, anisotropy parameters, orbit initial conditions, the absence of higher-order velocity moments, the spatial resolution, and the signal-to-noise ratio.

Modeling dynamic higher-order comoments for portfolio selection based on copula approach

This paper introduces a novel approach to estimating time-varying higher-order comoments from a theoretical standpoint. We present how to estimate the dynamic higher-order comoments of asset returns under the copula framework, which builds on the ARCD and copula-DCC models to capture the time variation in higher-order moments and correlations of asset returns. Additionally, the elements in the coskewness and cokurtosis matrices are calculated by the double, triple, and quadruple integrals associated with the joint density function of asset returns. The empirical application to five international market indexes shows that the portfolio with time-varying higher-order comoments estimated by the copula approach significantly outperforms equally weighted and mean–variance strategies in economic performance. The robustness analysis verifies the validity and robustness of the proposed estimation method. Our research offers fresh insights for portfolio analysis and risk management decision-making in practical scenarios.

Three-dimensional central-moment pseudopotential lattice Boltzmann model with improved discrete additional term

In this work, a three-dimensional central-moment pseudopotential lattice Boltzmann model is developed to simulate a two-phase flow and wetting phenomena. In this model, an improved discrete additional term is proposed to regulate the thermodynamic consistency and surface tension. Different from the discrete additional terms in previous models where only low-order terms are derived at the macroscopic Navier–Stokes equation level, high-order terms are correctly constructed at the mesoscopic lattice Boltzmann equation level in the present improved discrete additional term so that the high-order central moments can be modified in the collision step. With the improved discrete additional term, the simple relationship between the interaction force and the pseudopotential functions is well preserved. On this basis, a simplified wetting boundary scheme is further proposed, which eliminates the complex process for choosing proper characteristic vectors and interpolation. Numerical simulations demonstrate that the proposed model can achieve better performance in thermodynamic consistency, Galilean invariance, numerical stability and computational efficiency, and have great ability to simulate two-phase flow and wetting phenomena on realistic conditions.

Confounder-adjusted covariances of system outputs and applications to structural health monitoring

Automated damage detection is an integral component of each structural health monitoring (SHM) system. Typically, measurements from various sensors are collected and reduced to damage-sensitive features, and diagnostic values are generated by statistically evaluating the features. Since changes in data do not only result from damage, it is necessary to determine the confounding factors (environmental or operational variables) and to remove their effects from the measurements or features. Many existing methods for correcting confounding effects are based on different types of mean regression. This neglects potential changes in higher-order statistical moments, but in particular, the output covariances are essential for generating reliable diagnostics for damage detection. This article presents an approach to explicitly quantify the changes in the covariance, using conditional covariance matrices based on a non-parametric, kernel-based estimator. The method is applied to the Munich Test Bridge and the KW51 Railway Bridge in Leuven, covering both raw sensor measurements (acceleration, strain, inclination) and extracted damage-sensitive features (natural frequencies). The results show that covariances between different vibration or inclination sensors can significantly change due to temperature changes, and the same is true for natural frequencies. To highlight the advantages, it is explained how conditional covariances can be combined with standard approaches for damage detection, such as the Mahalanobis distance and principal component analysis. As a result, more reliable diagnostic values can be generated with fewer false alarms.

Box replication effects in weak lensing light-cone construction

Abstract Weak gravitational lensing simulations serve as indispensable tools for obtaining precise cosmological constraints. In particular, it is crucial to address the systematic uncertainties in theoretical predictions, given the rapid increase in galaxy numbers and the reduction in observational noise. Both on-the-fly and post-processing methods for constructing lensing light-cones encounter limitations due to the finite simulated volume, necessitating the replication of the simulation box to encompass the volume to high redshifts. To address this issue, our primary focus lies on investigating and quantifying the impact of box replication on the convergence power spectrum and higher-order moments of lensing fields. Subsequently, a univariate model is utilized to estimate the amplitude parameter A by fitting four statistics measured from partial-sky light-cones along specific angles, to the averaged result from random directions. The investigation demonstrates that the systematic bias stemming from the box replication phenomenon falls within the bounds of statistical errors for the majority of cases. However, caution should be exercised when considering high-order statistics on a small sky coverage (≲ 25 deg2). For this case, we have developed a code that facilitates the identification of optimal viewing angles for the light-cone construction. This code has been made publicly accessible https://github.com/czymh/losf.

Identification of bi-harmonic periodic signal contaminated with Gaussian random noise by analysing high-order PDF moments

Identification of bi-harmonic periodic signal contaminated with Gaussian random noise by analysing high-order PDF moments

Time-frequency higher-order moment Co-movement and connectedness between Chinese stock and commodity markets

This study examines the higher-order moment co-movement and connectedness between China's stock and commodity markets across time and frequency domains. We propose wavelet decomposition to develop a multiscale time-varying parameter vector autoregression (TVP-VAR) approach for measuring higher-order moment connectedness. Our empirical findings are as follows: First, the co-movement of stock-commodity varies over time and across different frequencies, exhibiting heterogeneity at different moments. Stocks demonstrate robust co-movement with commodities over the medium- and long-term periods. Second, higher-order moment connectedness is stronger than return connectedness, whereas weaker than volatility connectedness. Finally, higher-order moment connectedness is highly event-dependent, peaking at COVID-19 onset. And long-run factors have the greatest effect on dynamic moment connectedness.

Workflow Trace Profiling and Execution Time Analysis in Quantitative Verification

Workflows orchestrate a collection of computing tasks to form a complex workflow logic. Different from the traditional monolithic workflow management systems, modern workflow systems often manifest high throughput, concurrency and scalability. As service-based systems, execution time monitoring is an important part of maintaining the performance for those systems. We developed a trace profiling approach that leverages quantitative verification (also known as probabilistic model checking) to analyse complex time metrics for workflow traces. The strength of probabilistic model checking lies in the ability of expressing various temporal properties for a stochastic system model and performing automated quantitative verification. We employ semi-Makrov chains (SMCs) as the formal model and consider the first passage times (FPT) measures in the SMCs. Our approach maintains simple mergeable data summaries of the workflow executions and computes the moment parameters for FPT efficiently. We describe an application of our approach to AWS Step Functions, a notable workflow web service. An empirical evaluation shows that our approach is efficient for computer high-order FPT moments for sizeable workflows in practice. It can compute up to the fourth moment for a large workflow model with 10,000 states within 70 s.

Iterated rational quadratic kernel - High-order unscented Kalman filtering algorithm for spacecraft tracking

The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods. However, reentry flight is accompanied by complex flight environments, which brings to the uncertain, complex, and strongly coupled non-Gaussian detection noise. As a result, there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application. To address these issues, a new iterated rational quadratic (RQ) kernel high-order unscented Kalman filtering (IRQ-HUKF) algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed. Firstly, the characteristic analysis of the RQ kernel is investigated in detail, which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing high-order moments of the RQ kernel. Subsequently, the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion, termed the iterated RQ kernel-UKF (RQ-UKF) algorithm by derived analytically, which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing high-order moments and heavy-tailed characteristics. Meanwhile, to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems, the high-order Sigma Points (SP) as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF. Finally, to further improve the flexibility of the IRQ-HUKF algorithm in practical application, an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence (KLD) method and parametric sensitivity analysis of the RQ kernel. The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.

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.

Fast empirical scenarios

We seek to extract a small number of representative scenarios from large panel data that are consistent with sample moments. Among two novel algorithms, the first identifies scenarios that have not been observed before, and comes with a scenario-based representation of covariance matrices. The second proposal selects important data points from states of the world that have already realized, and are consistent with higher-order sample moment information. Both algorithms are efficient to compute and lend themselves to consistent scenario-based modeling and multi-dimensional numerical integration that can be used for interpretable decision-making under uncertainty. Extensive numerical benchmarking studies and an application in portfolio optimization favor the proposed algorithms.

On [formula omitted]-error moment stability and stabilization for discrete-time semi-Markov jump linear systems

In this paper, we study the σ-error moment stability and stabilization for a class of discrete-time semi-Markov jump linear systems (S-MJLS). It is shown that the existing results on σ-error moment stability for discrete-time S-MJLS can be obtained under weaker conditions, and based on the established stability results, the high-order moment stabilization problem is investigated for the first time.

Optimal Investments in the Portfolio Yield Reactive (PYR) Model

We evolved our past Portfolio Yield Reactive (PYR) model to provide a competitive system with infiltration of categorical information and fundamentals into advanced higher-order moments that support more objective portfolio selection aided by intelligent computing. The system of the PYR model searches for hidden corporate performance prototypes in big data from accounting and financial statements. The PYR model restricts malicious patterns, such as hoaxes, noise, and manipulation, incorporated into a novel optimal portfolio selection method.

Self-scaling generalized Townsend-Perry constants for high-order moments in turbulent boundary layers

Self-scaling generalized Townsend-Perry constants for high-order moments in turbulent boundary layers

Global Sensitivity Analysis via Optimal Transport

We examine the construction of variable importance measures for multivariate responses using the theory of optimal transport. We start with the classical optimal transport formulation. We show that the resulting sensitivity indices are well-defined under input dependence, are equal to zero under statistical independence, and are maximal under fully functional dependence. Also, they satisfy a continuity property for information refinements. We show that the new indices encompass Wagner’s variance-based sensitivity measures. Moreover, they provide deeper insights into the effect of an input’s uncertainty, quantifying its impact on the output mean, variance, and higher-order moments. We then consider the entropic formulation of the optimal transport problem and show that the resulting global sensitivity measures satisfy the same properties, with the exception that, under statistical independence, they are minimal, but not necessarily equal to zero. We prove the consistency of a given-data estimation strategy and test the feasibility of algorithmic implementations based on alternative optimal transport solvers. Application to the assemble-to-order simulator reveals a significant difference in the key drivers of uncertainty between the case in which the quantity of interest is profit (univariate) or inventory (multivariate). The new importance measures contribute to meeting the increasing demand for methods that make black-box models more transparent to analysts and decision makers. This paper was accepted by Baris Ata, stochastic models and simulation. Funding: A. Figalli acknowledges the support of the ERC [Grant 721675] “Regularity and Stability in Partial Differential Equations (RSPDE)” and of the Lagrange Mathematics and Computation Research Center. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.01796 .

Extreme spillovers across carbon and energy markets: A multiscale higher-order moment analysis

The complexity of carbon market mechanisms and the uncertainty in market conditions raise questions on how carbon and energy markets interact. The majority of existing studies focused on the lower-order moment spillover across carbon and energy markets, thereby posing limitations on carbon risk management and carbon market efficiency. This paper analyzes multiscale skewness and kurtosis spillovers across carbon and energy markets under different market conditions. It is found that carbon market is a short-term net skewness spillover receiver, but becomes a medium-term risk source under all market conditions, capable of transmitting skewness risk to the natural gas market. The carbon market acts as a short- and medium-term kurtosis risk source for the natural gas and electricity markets in the lower probability of extreme returns, but bears the kurtosis risk from the natural gas and coal markets when the extreme risk is high. These results indicate that policymakers should take measures to adjust carbon prices when facing long-term skewness risk and a lower probability of extreme returns in the carbon market, to prevent further spread of risk to the energy markets.