ARCHModels.jl: Estimating ARCH Models in Julia

This paper introduces ARCHModels.jl, a package for the Julia programming language that implements a number of univariate and multivariate autoregressive conditional heteroskedasticity models. This model class is the workhorse tool for modeling the conditional volatility of financial assets. The distinguishing feature of these models is that they model the latent volatility as a (deterministic) function of past returns and volatilities. This recursive structure results in loop-heavy code which, due to its just-in-time compiler, Julia is well-equipped to handle. As such, the entire package is written in Julia, without any binary dependencies. We benchmark the performance of ARCHModels.jl against popular implementations in MATLAB, R, and Python, and illustrate its use in a detailed case study

Multivariate Elliptical Truncated Moments

In this study, we derived analytic expressions for the elliptical truncated moment generating function (MGF), the zeroth, first, and second-order moments of quadratic forms of the multivariate normal, Student’s t, and generalised hyperbolic distributions. The resulting formulae were tested in a numerical application to calculate an analytic expression of the expected shortfall of quadratic portfolios with the benefit that moment based sensitivity measures can be derived from the analytic expression. The convergence rate of the analytic expression is fast – one iteration – for small closed integration domains, and slower for open integration domains when compared to the Monte Carlo integration method. The analytic formulae provide a theoretical framework for calculations in robust estimation, robust regression, outlier detection, design of experiments, and stochastic extensions of deterministic elliptical curves results

On quadratic forms in multivariate generalized hyperbolic random vectors

Countless test statistics can be written as quadratic forms in certain random vectors, or ratios thereof. Consequently, their distribution has received considerable attention in the literature. Except for a few special cases, no closed-form expression for the cdf exists, and one resorts to numerical methods. Traditionally the problem is analyzed under the assumption of joint Gaussianity; the algorithm that is usually employed is that of Imhof (1961). The present manuscript generalizes this result to the case of multivariate generalized hyperbolic random vectors. This exible distribution nests, among others, the multivariate t, Laplace, and variance gamma distributions. An expression for the first partial moment is also obtained, which plays a vital role in financial risk management. The proof involves a generalization of the classic inversion formula due to Gil-Pelaez (1951). Two numerical applications are considered: first, the finite-sample distribution of the two stage least squares estimator of a structural parameter. Second, the Value at Risk and expected shortfall of a quadratic portfolio with heavy-tailed risk factors. An empirical application is examined, in which a portfolio of Dow Jones Industrial Index stock options is optimized with respect to its expected shortfall. The results demonstrate the benefits of the analytical expression

Effects of Biological and Chemical Degradation on the Properties of Scots Pine Wood—Part I: Chemical Composition and Microstructure of the Cell Wall

Research on new conservation treatment for archaeological wood requires large amounts of wooden material. For this purpose, artificial wood degradation (biological—using brown-rot fungus Coniophora puteana, and chemical—using NaOH solution) under laboratory conditions was conducted to obtain an abundance of similar samples that mimic naturally degraded wood and can serve for comparative studies. However, knowledge about its properties is necessary to use this material for further study. In this study, the chemical composition and microstructure of degraded cell walls were investigated using FT-IR, XRD, helium pycnometry and nitrogen absorption methods. The results show that biological degradation caused the loss of hemicelluloses and celluloses, including the reduction in cellulose crystallinity, and led to lignin modification, while chemical degradation mainly depleted the amount of hemicelluloses and lignin, but also affected crystalline cellulose. These changes affected the cell wall microstructure, increasing both surface area and total pore volume. However, the chemical degradation produced a greater number of mesopores of smaller size compared to fungal decomposition. Both degradation processes weakened the cell wall’s mechanical strength, resulting in high shrinkage of degraded wood during air-drying. The results of the study suggest that degraded wood obtained under laboratory conditions can be a useful material for studies on new consolidants for archaeological wood

Effects of Biological and Chemical Degradation on the Properties of Scots Pine Wood—Part I: Chemical Composition and Microstructure of the Cell Wall

Research on new conservation treatment for archaeological wood requires large amounts of wooden material. For this purpose, artificial wood degradation (biological—using brown-rot fungus Coniophora puteana, and chemical—using NaOH solution) under laboratory conditions was conducted to obtain an abundance of similar samples that mimic naturally degraded wood and can serve for comparative studies. However, knowledge about its properties is necessary to use this material for further study. In this study, the chemical composition and microstructure of degraded cell walls were investigated using FT-IR, XRD, helium pycnometry and nitrogen absorption methods. The results show that biological degradation caused the loss of hemicelluloses and celluloses, including the reduction in cellulose crystallinity, and led to lignin modification, while chemical degradation mainly depleted the amount of hemicelluloses and lignin, but also affected crystalline cellulose. These changes affected the cell wall microstructure, increasing both surface area and total pore volume. However, the chemical degradation produced a greater number of mesopores of smaller size compared to fungal decomposition. Both degradation processes weakened the cell wall’s mechanical strength, resulting in high shrinkage of degraded wood during air-drying. The results of the study suggest that degraded wood obtained under laboratory conditions can be a useful material for studies on new consolidants for archaeological wood

Fine-structural distribution of MMP-2 and MMP-9 activities in the rat skeletal muscle upon training: a study by high-resolution in situ zymography

Matrix metalloproteinases (MMPs) are key regulators of extracellular matrix remodeling, but have also important intracellular targets. The purpose of this study was to examine the activity and subcellular localization of the gelatinases MMP-2 and MMP-9 in skeletal muscle of control and physically trained rats. In control hind limb muscle, the activity of the gelatinases was barely detectable. In contrast, after 5 days of intense exercise, in Soleus (Sol), but not Extensor digitorum longus (EDL) muscle, significant upregulation of gelatinolytic activity in myofibers was observed mainly in the nuclei, as assessed by high resolution in situ zymography. The nuclei of quiescent satellite cells did not contain the activity. Within the myonuclei, the gelatinolytic activity colocalized with an activated RNA Polymerase II. Also in Sol, but not in EDL, there were few foci of mononuclear cells with strongly positive cytoplasm, associated with apparent necrotic myofibers. These cells were identified as activated satellite cells/myoblasts. No extracellular gelatinase activity was observed. Gel zymography combined with subcellular fractionation revealed training-related upregulation of active MMP-2 in the nuclear fraction, and increase of active MMP-9 in the cytoplasmic fraction of Sol. Using RT-PCR, selective increase in MMP-9 mRNA was observed. We conclude that training activates nuclear MMP-2, and increases expression and activity of cytoplasmic MMP-9 in Sol, but not in EDL. Our results suggest that the gelatinases are involved in muscle adaptation to training, and that MMP-2 may play a novel role in myonuclear functions

Archmodels.Jl: Estimating Arch Models in Julia

This paper introduces ARCHModels.jl, a package for the Julia programming language that implements a number of univariate and multivariate ARCH-type models. This model class is the workhorse tool for modelling the conditional volatility of financial assets. Their distinguishing feature is that they model the latent volatility as a (deterministic) function of past returns and volatilities. This recursive structure results in loop-heavy code which, due to its just-in-time compiler, Julia is well-equipped to handle. As such, the entire package is written in Julia, without any binary dependencies. We benchmark the performance of ARCHModels.jl against popular implementations in MATLAB, R, and Python, and illustrate its use in a detailed case study

Multivariate Elliptical Truncated Moments

In this study, we derived analytic expressions for the elliptical truncated moment generating function (MGF), the zeroth, first, and second-order moments of quadratic forms of the multivariate normal, Student’s t, and generalised hyperbolic distributions. The resulting formulae were tested in a numerical application to calculate an analytic expression of the expected shortfall of quadratic portfolios with the benefit that moment based sensitivity measures can be derived from the analytic expression. The convergence rate of the analytic expression is fast – one iteration – for small closed integration domains, and slower for open integration domains when compared to the Monte Carlo integration method. The analytic formulae provide a theoretical framework for calculations in robust estimation, robust regression, outlier detection, design of experiments, and stochastic extensions of deterministic elliptical curves results