GARCH Models under Power Transformed Returns: Empirical Evidence from International Stock Indices

This study evaluates the empirical performance of four power transformation families: extended Tukey, Modulus, Exponential, and Yeo--Johnson, in modeling the return in the context of GARCH(1,1) models with two error distributions: Gaussian (normal) and Student-t. We employ an Adaptive Random Walk Metropolis method in Markov Chain Monte Carlo scheme to draw parameters. Using 19 international stock indices from the Oxford-Man Institute and basing on the log likelihood, Akaike Information Criterion, Bayesian Information Criterion, and Deviance Information Criterion, the use of power transformation families to the return series clearly improves the fit of the normal GARCH(1,1) model. In particular, the Modulus transformation family provides the best fit. Under Student's t-error distribution assumption, the GARCH(1,1) models under power transformed returns perform better in few cases.

Possible ternary fission of super-heavy nuclei

In super-heavy nuclei, we may expect to discover new phenomena because of the strong Coulomb force. One example is the true ternary fission. We study the sequential two binary fission of 300120 and 252Cf that produces three fragments. We use the Metropolis method to estimate the probability of the second fission. The probability of the second fission is 10−4-10−3 for superheavy nuclei while it is 10−7−10−6 for heavy actinide nuclei. The most probable mass division is almost symmetric in the case of 300120. We also demonstrate the applicability of the Metropolis method to a non-equilibrium process by comparing it with the Langevin equation.

Energy of a quantum Coulomb liquid

ABSTRACT Using the Metropolis method to compute path integrals, the energy of a quantum strongly coupled Coulomb liquid (1 ≤ Γ ≤ 175), composed of distinguishable atomic nuclei and a uniform incompressible electron background, is calculated from first principles. The range of temperatures and densities considered represents fully ionized layers of white dwarfs and neutron stars. In particular, the results allow one to determine reliably the heat capacity of ions in dense fluid stellar matter, which is a crucial ingredient for modelling the thermal evolution of compact degenerate stars.

SEISMIC TOMOGRAPHY USING METROPOLIS METHOD OF VELOCITY FIELDS PARAMETERIZED BY HAAR WAVELET SERIES

ABSTRACT. The representation of compressional seismic waves velocity fields from geological models through numerical parameters has a strong geophysical importance, because, it makes possible to quantify such qualitative models, allowing its mathematical manipulation. In this way, the parameterization by Haar wavelet series may be seen as an attractive alternative.Keywords: parameterization, Haar wavelet series, pyramid algorithm, seismic tomography, seismic velocity field, traveltime data, Metropolis method. RESUMO. A representação de campos de velocidades sísmicas compressionais, através de parâmetros numéricos, é de importância básica na geofísica, pois torna possível a quantificação de modelos, antes qualitativos, permitindo assim que sejam matematicamente manipulados. A parametrização por série ondaleta Haar pode ser vista como uma alternativa atrativa para quantificar tais modelos...Palavras-chave: parametrização, série ondaleta Haar, inversão sísmica tomográfica, campo de velocidade sísmica, dados de tempo de trânsito, método Metropolis.

A sequential Bayesian approach for the estimation of the age–depth relationship of the Dome Fuji ice core

A technique for estimating the age–depth relationship in an ice core and evaluating its uncertainty is presented. The age–depth relationship is determined by the accumulation of snow at the site of the ice core and the thinning process as a result of the deformation of ice layers. However, since neither the accumulation rate nor the thinning process is fully known, it is essential to incorporate observational information into a model that describes the accumulation and thinning processes. In the proposed technique, the age as a function of depth is estimated by making use of age markers and δ18O data. The age markers provide reliable age information at several depths. The data of δ18O are used as a proxy of the temperature for estimating the accumulation rate. The estimation is achieved using the particle Markov chain Monte Carlo (PMCMC) method, which is a combination of the sequential Monte Carlo (SMC) method and the Markov chain Monte Carlo method. In this hybrid method, the posterior distributions for the parameters in the models for the accumulation and thinning process are computed using the Metropolis method, in which the likelihood is obtained with the SMC method, and the posterior distribution for the age as a function of depth is obtained by collecting the samples generated by the SMC method with Metropolis iterations. The use of this PMCMC method enables us to estimate the age–depth relationship without assuming either linearity or Gaussianity. The performance of the proposed technique is demonstrated by applying it to ice core data from Dome Fuji in Antarctica.

Study of switching in spin transition compounds within the mechanoelastic model with realistic parameters

Thermal hysteresis loop calculated using the Monte Carlo Metropolis method and snapshots of the system just before percolation, showing clusters of the same spin state molecules near corners. Variation of the compression of the connecting spring while a molecule i flips from the LS to the HS state.

A sequential Bayesian approach for the estimation of the age–depth relationship of Dome Fuji ice core

A technique for estimating the age–depth relationship in an ice core and evaluating its uncertainty is presented. The age–depth relationship is mainly determined by the accumulation of snow at the site of the ice core and the thinning process due to the horizontal stretching and vertical compression of ice layers. However, since neither the accumulation process nor the thinning process are fully understood, it is essential to incorporate observational information into a model that describes the accumulation and thinning processes. In the proposed technique, the age as a function of depth is estimated from age markers and δ18O data. The estimation is achieved using the particle Markov chain Monte Carlo (PMCMC) method, in which the sequential Monte Carlo (SMC) method is combined with the Markov chain Monte Carlo method. In this hybrid method, the posterior distributions for the parameters in the models for the accumulation and thinning processes are computed using the Metropolis method, in which the likelihood is obtained with the SMC method. Meanwhile, the posterior distribution for the age as a function of depth is obtained by collecting the samples generated by the SMC method with Metropolis iterations. The use of this PMCMC method enables us to estimate the age–depth relationship without assuming either linearity or Gaussianity. The performance of the proposed technique is demonstrated by applying it to ice core data from Dome Fuji in Antarctica.

A HIERARCHICAL BAYESIAN ANALYSIS OF HORSE RACING

Horse racing is the most popular sport in Hong Kong. Nowhere else in the world is such attention paid to the races and such large sums of money bet. It is literally a “national sport”. Popular literature has many stories about computerized “betting teams” winning fortunes by using statistical analysis.[1] Additionally, numerous academic papers have been published on the subject, implementing a variety of statistical methods. The academic justification for these papers is that a parimutuel game represents a study in decisions under uncertainty, efficiency of markets, and even investor psychology. A review of the available published literature has failed to find any Bayesian approach to this modeling challenge.This study will attempt to predict the running speed of a horse in a given race. To that effect, the coefficients of a linear model are estimated using the Bayesian method of Markov Chain Monte Carlo. Two methods of computing the sampled posterior are used and their results compared. The Gibbs method assumes that all the coefficients are normally distributed, while the Metropolis method allows for their distribution to have an unknown shape. I will calculate and compare the predictive results of several models using these Bayesian Methods.