Mathematical and Computational Applications

17 pages, 508 KiB

Open AccessArticle

Theory of Functional Connections Applied to Linear ODEs Subject to Integral Constraints and Linear Ordinary Integro-Differential Equations

by Mario De Florio, Enrico Schiassi, Andrea D’Ambrosio, Daniele Mortari and Roberto Furfaro

Math. Comput. Appl. 2021, 26(3), 65; https://doi.org/10.3390/mca26030065 - 12 Sep 2021

Cited by 12 | Viewed by 2618

Abstract

This study shows how the Theory of Functional Connections (TFC) allows us to obtain fast and highly accurate solutions to linear ODEs involving integrals. Integrals can be constraints and/or terms of the differential equations (e.g., ordinary integro-differential equations). This study first summarizes TFC, [...] Read more.

This study shows how the Theory of Functional Connections (TFC) allows us to obtain fast and highly accurate solutions to linear ODEs involving integrals. Integrals can be constraints and/or terms of the differential equations (e.g., ordinary integro-differential equations). This study first summarizes TFC, a mathematical procedure to obtain constrained expressions. These are functionals representing all functions satisfying a set of linear constraints. These functionals contain a free function,

g (x)

, representing the unknown function to optimize. Two numerical approaches are shown to numerically estimate

g (x)

. The first models

g (x)

as a linear combination of a set of basis functions, such as Chebyshev or Legendre orthogonal polynomials, while the second models

g (x)

as a neural network. Meaningful problems are provided. In all numerical problems, the proposed method produces very fast and accurate solutions. Full article

(This article belongs to the Section Engineering)

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27 pages, 8314 KiB

Open AccessArticle

A Hybrid Estimation of Distribution Algorithm for the Quay Crane Scheduling Problem

by Ricardo Pérez-Rodríguez

Math. Comput. Appl. 2021, 26(3), 64; https://doi.org/10.3390/mca26030064 - 10 Sep 2021

Cited by 4 | Viewed by 2239

Abstract

The aim of the quay crane scheduling problem (QCSP) is to identify the best sequence of discharging and loading operations for a set of quay cranes. This problem is solved with a new hybrid estimation of distribution algorithm (EDA). The approach is proposed [...] Read more.

The aim of the quay crane scheduling problem (QCSP) is to identify the best sequence of discharging and loading operations for a set of quay cranes. This problem is solved with a new hybrid estimation of distribution algorithm (EDA). The approach is proposed to tackle the drawbacks of the EDAs, i.e., the lack of diversity of solutions and poor ability of exploitation. The hybridization approach, used in this investigation, uses a distance based ranking model and the moth-flame algorithm. The distance based ranking model is in charge of modelling the solution space distribution, through an exponential function, by measuring the distance between solutions; meanwhile, the heuristic moth-flame determines who would be the offspring, with a spiral function that identifies the new locations for the new solutions. Based on the results, the proposed scheme, called QCEDA, works to enhance the performance of those other EDAs that use complex probability models. The dispersion results of the QCEDA scheme are less than the other algorithms used in the comparison section. This means that the solutions found by the QCEDA are more concentrated around the best value than other algorithms, i.e., the average of the solutions of the QCEDA converges better than other approaches to the best found value. Finally, as a conclusion, the hybrid EDAs have a better performance, or equal in effectiveness, than the so called pure EDAs. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)

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18 pages, 1115 KiB

Open AccessArticle

On the Elicitability and Risk Model Comparison of Emerging Markets Equities

by Peterson Owusu Junior, Imhotep Paul Alagidede and Aviral Kumar Tiwari

Math. Comput. Appl. 2021, 26(3), 63; https://doi.org/10.3390/mca26030063 - 06 Sep 2021

Cited by 2 | Viewed by 2116

Abstract

The need for comparative backtesting in the Basel III framework presents the challenge for ranking of internal value-at-risk (VaR) and expected shortfall (ES) models. We use a joint loss function to score the elicitable joint VaR and ES models to select competing tail [...] Read more.

The need for comparative backtesting in the Basel III framework presents the challenge for ranking of internal value-at-risk (VaR) and expected shortfall (ES) models. We use a joint loss function to score the elicitable joint VaR and ES models to select competing tail risk models for the top 9 emerging markets equities and the emerging markets composite index. We achieve this with the model confidence set (MCS) procedure. Our analysis span two sub-sample periods representing turbulent (Eurozone and Global Financial crises periods) and tranquil (post-Global Financial crisis period) market conditions. We find that many of the markets risk models are time-invariant and independent of market conditions. But for China and South Africa this is not true because their risk models are time-varying, market conditions-dependent, percentile-dependent and heterogeneous. Tail risk modelling may be difficult compared to other markets. The resemblance between China and South Africa can stem from the closeness between their equities composition. However, generally, there is evidence of more homogeneity than heterogeneity in risk models. This is indicated by a minimum of three models (out of six) per equity in most of the countries. This may ease the burden for risk managers to find the optimal set of models. Our study is important for internal risk modelling, regulatory oversight, reduce regulatory arbitrage and may bolster confidence in international investors with respect to emerging markets equities. Full article

(This article belongs to the Special Issue Mathematical and Computational Applications in Finance and Economics)

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22 pages, 470 KiB

Open AccessArticle

On a Special Weighted Version of the Odd Weibull-Generated Class of Distributions

by Zichuan Mi, Saddam Hussain and Christophe Chesneau

Math. Comput. Appl. 2021, 26(3), 62; https://doi.org/10.3390/mca26030062 - 29 Aug 2021

Cited by 1 | Viewed by 2081

Abstract

In recent advances in distribution theory, the Weibull distribution has often been used to generate new classes of univariate continuous distributions. They find many applications in important disciplines such as medicine, biology, engineering, economics, informatics, and finance; their usefulness is synonymous with success. [...] Read more.

In recent advances in distribution theory, the Weibull distribution has often been used to generate new classes of univariate continuous distributions. They find many applications in important disciplines such as medicine, biology, engineering, economics, informatics, and finance; their usefulness is synonymous with success. In this study, a new Weibull-generated-type class is presented, called the weighted odd Weibull generated class. Its definition is based on a cumulative distribution function, which combines a specific weighted odd function with the cumulative distribution function of the Weibull distribution. This weighted function was chosen to make the new class a real alternative in the first-order stochastic sense to two of the most famous existing Weibull generated classes: the Weibull-G and Weibull-H classes. Its mathematical properties are provided, leading to the study of various probabilistic functions and measures of interest. In a consequent part of the study, the focus is on a special three-parameter survival distribution of the new class defined with the standard exponential distribution as a reference. The exploratory analysis reveals a high level of adaptability of the corresponding probability density and hazard rate functions; the curves of the probability density function can be decreasing, reversed N shaped, and unimodal with heterogeneous skewness and tail weight properties, and the curves of the hazard rate function demonstrate increasing, decreasing, almost constant, and bathtub shapes. These qualities are often required for diverse data fitting purposes. In light of the above, the corresponding data fitting methodology has been developed; we estimate the model parameters via the likelihood function maximization method, the efficiency of which is proven by a detailed simulation study. Then, the new model is applied to engineering and environmental data, surpassing several generalizations or extensions of the exponential model, including some derived from established Weibull-generated classes; the Weibull-G and Weibull-H classes are considered. Standard criteria give credit to the proposed model; for the considered data, it is considered the best. Full article

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23 pages, 5380 KiB

Open AccessArticle

New Stable, Explicit, Shifted-Hopscotch Algorithms for the Heat Equation

by Ádám Nagy, Mahmoud Saleh, Issa Omle, Humam Kareem and Endre Kovács

Math. Comput. Appl. 2021, 26(3), 61; https://doi.org/10.3390/mca26030061 - 26 Aug 2021

Cited by 15 | Viewed by 2596

Abstract

Our goal was to find more effective numerical algorithms to solve the heat or diffusion equation. We created new five-stage algorithms by shifting the time of the odd cells in the well-known odd-even hopscotch algorithm by a half time step and applied different [...] Read more.

Our goal was to find more effective numerical algorithms to solve the heat or diffusion equation. We created new five-stage algorithms by shifting the time of the odd cells in the well-known odd-even hopscotch algorithm by a half time step and applied different formulas in different stages. First, we tested 10⁵ = 100,000 different algorithm combinations in case of small systems with random parameters, and then examined the competitiveness of the best algorithms by testing them in case of large systems against popular solvers. These tests helped us find the top five combinations, and showed that these new methods are, indeed, effective since quite accurate and reliable results were obtained in a very short time. After this, we verified these five methods by reproducing a recently found non-conventional analytical solution of the heat equation, then we demonstrated that the methods worked for nonlinear problems by solving Fisher’s equation. We analytically proved that the methods had second-order accuracy, and also showed that one of the five methods was positivity preserving and the others also had good stability properties. Full article

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20 pages, 844 KiB

Open AccessArticle

Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling

by Ahmad Abushaikha, Dominique Guérillot, Mostafa Kadiri and Saber Trabelsi

Math. Comput. Appl. 2021, 26(3), 60; https://doi.org/10.3390/mca26030060 - 25 Aug 2021

Viewed by 1724

Abstract

This paper is dedicated to the modeling, analysis, and numerical simulation of a two-phase non-Darcian flow through a porous medium with phase-coupling. Specifically, we introduce an extended Forchheimer–Darcy model where the interaction between phases is taken into consideration. From the modeling point of [...] Read more.

This paper is dedicated to the modeling, analysis, and numerical simulation of a two-phase non-Darcian flow through a porous medium with phase-coupling. Specifically, we introduce an extended Forchheimer–Darcy model where the interaction between phases is taken into consideration. From the modeling point of view, the extension consists of the addition to each phase equation of a term depending on the gradient of the pressure of the other phase, leading to a coupled system of differential equations. The obtained system is much more involved than the classical Darcy system since it involves the Forchheimer equation in addition to the Darcy one. This model is more appropriate when there is a substantial difference between the phases’ velocities, for instance in the case of gas/water phases, and applications in oil recovery using gas flooding. Based on the Buckley–Leverett theory, including capillary pressure, we derive an explicit expression of the phases’ velocities and fractional water flows in terms of the gradient of the capillary pressure, and the total constant velocity. Various scenarios are considered, and the respective numerical simulations are presented. In particular, comparisons with the classical models (without phase coupling) are provided in terms of breakthrough time among others. Eventually, we provide a post-processing method for the derivation of the solution of the new coupled system using the classical non-coupled system. This method is of interest for industry since it allows for including the phase coupling approach in existing numerical codes and software (designed for solving classical models) without major technical changes. Full article

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15 pages, 292 KiB

Open AccessArticle

A Phase-Fitted and Amplification-Fitted Explicit Runge–Kutta–Nyström Pair for Oscillating Systems

by Musa Ahmed Demba, Higinio Ramos, Poom Kumam and Wiboonsak Watthayu

Math. Comput. Appl. 2021, 26(3), 59; https://doi.org/10.3390/mca26030059 - 24 Aug 2021

Cited by 2 | Viewed by 1522

Abstract

An optimized embedded 5(3) pair of explicit Runge–Kutta–Nyström methods with four stages using phase-fitted and amplification-fitted techniques is developed in this paper. The new adapted pair can exactly integrate (except round-off errors) the common test:

y^{″} = - w^{2} y

. [...] Read more.

An optimized embedded 5(3) pair of explicit Runge–Kutta–Nyström methods with four stages using phase-fitted and amplification-fitted techniques is developed in this paper. The new adapted pair can exactly integrate (except round-off errors) the common test:

y^{″} = - w^{2} y

. The local truncation error of the new method is derived, and we show that the order of convergence is maintained. The stability analysis is addressed, and we demonstrate that the developed method is absolutely stable, and thus appropriate for solving stiff problems. The numerical experiments show a better performance of the new embedded pair in comparison with other existing RKN pairs of similar characteristics. Full article

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10 pages, 286 KiB

Open AccessArticle

Definite Integral Involving Rational Functions of Powers and Exponentials Expressed in Terms of the Lerch Function

by Robert Reynolds and Allan Stauffer

Math. Comput. Appl. 2021, 26(3), 58; https://doi.org/10.3390/mca26030058 - 18 Aug 2021

Viewed by 1321

Abstract

This paper gives new integrals related to a class of special functions. This paper also showcases the derivation of definite integrals involving the quotient of functions with powers and the exponential function expressed in terms of the Lerch function and special cases involving [...] Read more.

This paper gives new integrals related to a class of special functions. This paper also showcases the derivation of definite integrals involving the quotient of functions with powers and the exponential function expressed in terms of the Lerch function and special cases involving fundamental constants. The goal of this paper is to expand upon current tables of definite integrals with the aim of assisting researchers in need of new integral formulae. Full article

10 pages, 307 KiB

Open AccessArticle

Using the Evolution Operator to Classify Evolution Algebras

by Desamparados Fernández-Ternero, Víctor M. Gómez-Sousa and Juan Núñez-Valdés

Math. Comput. Appl. 2021, 26(3), 57; https://doi.org/10.3390/mca26030057 - 05 Aug 2021

Cited by 2 | Viewed by 1511

Abstract

Evolution algebras are currently widely studied due to their importance not only “per se” but also for their many applications to different scientific disciplines, such as Physics or Engineering, for instance. This paper deals with these types of algebras and their applications. A [...] Read more.

Evolution algebras are currently widely studied due to their importance not only “per se” but also for their many applications to different scientific disciplines, such as Physics or Engineering, for instance. This paper deals with these types of algebras and their applications. A criterion for classifying those satisfying certain conditions is given and an algorithm to obtain degenerate evolution algebras starting from those of smaller dimensions is also analyzed and constructed. Full article

(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications 2021)

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17 pages, 2903 KiB

Open AccessFeature PaperArticle

Preserving Geo-Indistinguishability of the Emergency Scene to Predict Ambulance Response Time

by Héber H. Arcolezi, Selene Cerna, Christophe Guyeux and Jean-François Couchot

Math. Comput. Appl. 2021, 26(3), 56; https://doi.org/10.3390/mca26030056 - 04 Aug 2021

Cited by 6 | Viewed by 4187

Abstract

Emergency medical services (EMS) provide crucial emergency assistance and ambulatory services. One key measurement of EMS’s quality of service is their ambulances’ response time (ART), which generally refers to the period between EMS notification and the moment an ambulance arrives on the scene. [...] Read more.

Emergency medical services (EMS) provide crucial emergency assistance and ambulatory services. One key measurement of EMS’s quality of service is their ambulances’ response time (ART), which generally refers to the period between EMS notification and the moment an ambulance arrives on the scene. Due to many victims requiring care within adequate time (e.g., cardiac arrest), improving ARTs is vital. This paper proposes to predict ARTs using machine-learning (ML) techniques, which could be used as a decision-support system by EMS to allow a dynamic selection of ambulance dispatch centers. However, one well-known predictor of ART is the location of the emergency (e.g., if it is urban or rural areas), which is sensitive data because it can reveal who received care and for which reason. Thus, we considered the ‘input perturbation’ setting in the privacy-preserving ML literature, which allows EMS to sanitize each location data independently and, hence, ML models are trained only with sanitized data. In this paper, geo-indistinguishability was applied to sanitize each emergency location data, which is a state-of-the-art formal notion based on differential privacy. To validate our proposals, we used retrospective data of an EMS in France, namely Departmental Fire and Rescue Service of Doubs, and publicly available data (e.g., weather and traffic data). As shown in the results, the sanitization of location data and the perturbation of its associated features (e.g., city, distance) had no considerable impact on predicting ARTs. With these findings, EMSs may prefer using and/or sharing sanitized datasets to avoid possible data leakages, membership inference attacks, or data reconstructions, for example. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)

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11 pages, 327 KiB

Open AccessArticle

Some Aspects of Numerical Analysis for a Model Nonlinear Fractional Variable Order Equation

by Roman Parovik and Dmitriy Tverdyi

Math. Comput. Appl. 2021, 26(3), 55; https://doi.org/10.3390/mca26030055 - 29 Jul 2021

Cited by 7 | Viewed by 1688

Abstract

The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of a nonlinear, ordinary differential equation with a derivative of a fractional variable order of the Gerasimov–Caputo type. The questions of approximation, convergence, and stability of this scheme are studied. It [...] Read more.

The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of a nonlinear, ordinary differential equation with a derivative of a fractional variable order of the Gerasimov–Caputo type. The questions of approximation, convergence, and stability of this scheme are studied. It is shown that the nonlocal finite-difference scheme is conditionally stable and converges to the first order. Using the fractional Riccati equation as an example, the computational accuracy of the numerical method is analyzed. It is shown that with an increase in the nodes of the computational grid, the order of computational accuracy tends to unity, i.e., to the theoretical value of the order of accuracy. Full article

(This article belongs to the Section Natural Sciences)

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10 pages, 493 KiB

Open AccessFeature PaperArticle

Alternative Initial Probability Tables for Elicitation of Bayesian Belief Networks

by Frank Phillipson, Peter Langenkamp and Reinder Wolthuis

Math. Comput. Appl. 2021, 26(3), 54; https://doi.org/10.3390/mca26030054 - 28 Jul 2021

Viewed by 2053

Abstract

Bayesian Belief Networks are used in many fields of application. Defining the conditional dependencies via conditional probability tables requires the elicitation of expert belief to fill these tables, which grow very large quickly. In this work, we propose two methods to prepare these [...] Read more.

Bayesian Belief Networks are used in many fields of application. Defining the conditional dependencies via conditional probability tables requires the elicitation of expert belief to fill these tables, which grow very large quickly. In this work, we propose two methods to prepare these tables based on a low number of input parameters using specific structures and one method to generate the table using probability tables of each relation of a child node with a certain parent. These tables can be used further as a starting point for elicitation. Full article

(This article belongs to the Section Engineering)

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10 pages, 473 KiB

Open AccessArticle

Solving a Real-Life Distributor’s Pallet Loading Problem

by Mauro Dell’Amico and Matteo Magnani

Math. Comput. Appl. 2021, 26(3), 53; https://doi.org/10.3390/mca26030053 - 19 Jul 2021

Cited by 4 | Viewed by 3292

Abstract

We consider the distributor’s pallet loading problem where a set of different boxes are packed on the smallest number of pallets by satisfying a given set of constraints. In particular, we refer to a real-life environment where each pallet is loaded with a [...] Read more.

We consider the distributor’s pallet loading problem where a set of different boxes are packed on the smallest number of pallets by satisfying a given set of constraints. In particular, we refer to a real-life environment where each pallet is loaded with a set of layers made of boxes, and both a stability constraint and a compression constraint must be respected. The stability requirement imposes the following: (a) to load at level

k + 1

a layer with total area (i.e., the sum of the bottom faces’ area of the boxes present in the layer) not exceeding

α

times the area of the layer of level k (where

α \geq 1

), and (b) to limit with a given threshold the difference between the highest and the lowest box of a layer. The compression constraint defines the maximum weight that each layer k can sustain; hence, the total weight of the layers loaded over k must not exceed that value. Some stability and compression constraints are considered in other works, but to our knowledge, none are defined as faced in a real-life problem. We present a matheuristic approach which works in two phases. In the first, a number of layers are defined using classical 2D bin packing algorithms, applied to a smart selection of boxes. In the second phase, the layers are packed on the minimum number of pallets by means of a specialized MILP model solved with Gurobi. Computational experiments on real-life instances are used to assess the effectiveness of the algorithm. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)

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25 pages, 1753 KiB

Open AccessFeature PaperArticle

Applying the Swept Rule for Solving Two-Dimensional Partial Differential Equations on Heterogeneous Architectures

by Anthony S. Walker and Kyle E. Niemeyer

Math. Comput. Appl. 2021, 26(3), 52; https://doi.org/10.3390/mca26030052 - 17 Jul 2021

Cited by 1 | Viewed by 2067

Abstract

The partial differential equations describing compressible fluid flows can be notoriously difficult to resolve on a pragmatic scale and often require the use of high-performance computing systems and/or accelerators. However, these systems face scaling issues such as latency, the fixed cost of communicating [...] Read more.

The partial differential equations describing compressible fluid flows can be notoriously difficult to resolve on a pragmatic scale and often require the use of high-performance computing systems and/or accelerators. However, these systems face scaling issues such as latency, the fixed cost of communicating information between devices in the system. The swept rule is a technique designed to minimize these costs by obtaining a solution to unsteady equations at as many possible spatial locations and times prior to communicating. In this study, we implemented and tested the swept rule for solving two-dimensional problems on heterogeneous computing systems across two distinct systems and three key parameters: problem size, GPU block size, and work distribution. Our solver showed a speedup range of 0.22–2.69 for the heat diffusion equation and 0.52–1.46 for the compressible Euler equations. We can conclude from this study that the swept rule offers both potential for speedups and slowdowns and that care should be taken when designing such a solver to maximize benefits. These results can help make decisions to maximize these benefits and inform designs. Full article

(This article belongs to the Section Engineering)

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19 pages, 803 KiB

Open AccessFeature PaperArticle

A Novel Reconstruction Method to Increase Spatial Resolution in Electron Probe Microanalysis

by Tamme Claus, Jonas Bünger and Manuel Torrilhon

Math. Comput. Appl. 2021, 26(3), 51; https://doi.org/10.3390/mca26030051 - 14 Jul 2021

Cited by 1 | Viewed by 1836

Abstract

The spatial resolution of electron probe microanalysis (EPMA), a non-destructive method to determine the chemical composition of materials, is currently restricted to a pixel size larger than the volume of interaction between beam electrons and the material, as a result of limitations on [...] Read more.

The spatial resolution of electron probe microanalysis (EPMA), a non-destructive method to determine the chemical composition of materials, is currently restricted to a pixel size larger than the volume of interaction between beam electrons and the material, as a result of limitations on the underlying k-ratio model. Using more sophisticated models to predict k-ratios while solving the inverse problem of reconstruction offers a possibility to increase the spatial resolution. Here, a k-ratio model based on the deterministic M1-model in Boltzmann Continuous Slowing-Down approximation (BCSD) will be utilized to present a reconstruction method for EPMA which is implemented as a PDE-constrained optimization problem. Iterative gradient-based optimization techniques are used in combination with the adjoint state method to calculate the gradient in order to solve the optimization problem efficiently. The accuracy of the spatial resolution still depends on the number and quality of the measured data, but in contrast to conventional reconstruction methods, an overlapping of the interaction volumes of different measurements is permissible without ambiguous solutions. The combination of k-ratios measured with various electron beam configurations is necessary for a high resolution. Attempts to reconstruct materials with synthetic data show challenges that occur with small reconstruction pixels, but also indicate the potential to improve the spatial resolution in EPMA using the presented method. Full article

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2 pages, 193 KiB

Open AccessEditorial

Numerical Modelling and Simulation Applied to Head Trauma

by Fábio A. O. Fernandes and Mariusz Ptak

Math. Comput. Appl. 2021, 26(3), 50; https://doi.org/10.3390/mca26030050 - 02 Jul 2021

Cited by 2 | Viewed by 1467

Abstract

Traumatic brain injury (TBI) is one of the leading causes of death and disability [...] Full article

(This article belongs to the Special Issue Numerical Modelling and Simulation Applied to Head Trauma)

13 pages, 665 KiB

Open AccessArticle

Uncertainty, Spillovers, and Forecasts of the Realized Variance of Gold Returns

by Rangan Gupta and Christian Pierdzioch

Math. Comput. Appl. 2021, 26(3), 49; https://doi.org/10.3390/mca26030049 - 02 Jul 2021

Viewed by 1969

Abstract

Using data for the group of G7 countries and China for the sample period 1996Q1 to 2020Q4, we study the role of uncertainty and spillovers for the out-of-sample forecasting of the realized variance of gold returns and its upside (good) and downside (bad) [...] Read more.

Using data for the group of G7 countries and China for the sample period 1996Q1 to 2020Q4, we study the role of uncertainty and spillovers for the out-of-sample forecasting of the realized variance of gold returns and its upside (good) and downside (bad) counterparts. We go beyond earlier research in that we do not focus exclusively on U.S.-based measures of uncertainty, and in that we account for international spillovers of uncertainty. Our results, based on the Lasso estimator, show that, across the various model configurations that we study, uncertainty has a more systematic effect on out-of-sample forecast accuracy than spillovers. Our results have important implications for investors in terms of, for example, pricing of related derivative securities and the development of portfolio-allocation strategies. Full article

(This article belongs to the Special Issue Mathematical and Computational Applications in Finance and Economics)

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Math. Comput. Appl., Volume 26, Issue 3 (September 2021) – 17 articles

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