Looking for skewness in financial time series

Summary In this paper, we study marginal and conditional skewness in financial returns for nine time series of major international stock indices. For this purpose, we develop a new variant of the GARCH model with dynamic skewness and kurtosis. Our empirical results indicate that there is no evidence of marginal asymmetry in the nine time series under consideration. We do however find significant time‐varying conditional skewness. The economic significance of conditional skewness is analysed in terms of Value‐at‐Risk measures and Market Risk Capital Requirements set by the Basel Accord.     

Construction of the World Health Organization child growth standards: selection of methods for attained growth curves

The World Health Organization (WHO), in collaboration with a number of research institutions worldwide, is developing new child growth standards. As part of a broad consultative process for selecting the best statistical methods, WHO convened a group of statisticians and child growth experts to review available methods, develop a strategy for assessing their strengths and weaknesses, and discuss methodological issues likely to be faced in the process of constructing the new growth curves. To select the method(s) to be used, the group proposed a two-stage decision-making process. First, to select a few relevant methods based on a list of set criteria and, second, to compare the methods using available tests or other established procedures. The group reviewed 30 methods for attained growth curves. Using the pre-defined criteria, a few were selected combining five distributions and two smoothing techniques. Because the number of selected methods was considered too large to be fully tested, a preliminary study was recommended to evaluate goodness of fit of the five distributions. Methods based on distributions with poor performance will be eliminated and the remaining methods fully tested and compared.     

Score confidence intervals and sample sizes for stratified comparisons of binomial proportions

In a series of articles, Gart and Nam construct the efficient score tests and confidence intervals with or without skewness correction for stratified comparisons of binomial proportions on the risk difference, relative risk, and odds ratio effect metrics. However, the stratified score methods and their properties are not well understood. We rederive the efficient score tests, which reveals their theoretical relationship with the contrast-based score tests, and provides a basis for adapting the method by using other weighting schemes. The inverse variance weight is optimal for a common treatment effect in large samples. We explore the behavior of the score approach in the presence of extreme outcomes when either no or all subjects in some strata are responders, and provide guidance on the choice of weights in the analysis of rare events. The score method is recommended for studies with a small number of moderate or large sized strata. A general framework is proposed to calculate the asymptotic power and sample size for the score test in superiority, noninferiority and equivalence clinical trials, or case-control studies. We also describe a nearly exact procedure that underestimates the exact power, but the degree of underestimation can be controlled to a negligible level. The proposed methods are illustrated by numerical examples.     

Linear mixed models for skew‐normal/independent bivariate responses with an application to periodontal disease

Bivariate clustered (correlated) data often encountered in epidemiological and clinical research are routinely analyzed under a linear mixed model (LMM) framework with underlying normality assumptions of the random effects and within‐subject errors. However, such normality assumptions might be questionable if the data set particularly exhibits skewness and heavy tails. Using a Bayesian paradigm, we use the skew‐normal/independent (SNI) distribution as a tool for modeling clustered data with bivariate non‐normal responses in an LMM framework. The SNI distribution is an attractive class of asymmetric thick‐tailed parametric structure which includes the skew‐normal distribution as a special case. We assume that the random effects follow multivariate SNI distributions and the random errors follow SNI distributions which provides substantial robustness over the symmetric normal process in an LMM framework. Specific distributions obtained as special cases, viz. the skew‐t, the skew‐slash and the skew‐contaminated normal distributions are compared, along with the default skew‐normal density. The methodology is illustrated through an application to a real data which records the periodontal health status of an interesting population using periodontal pocket depth (PPD) and clinical attachment level (CAL). Copyright © 2010 John Wiley & Sons, Ltd.     

Log transformation: application and interpretation in biomedical research

The log transformation has been widely used in biomedical research to deal with the skewed data. However, in the medical publications, we have found many misuses and misinterpretations of analysis based on log‐transformed data. In this paper, we list some common scenarios of misuse and misinterpretation of log transformation in biomedical applications. We also provide both theoretical and practical justifications to support our viewpoints. Copyright © 2012 John Wiley & Sons, Ltd.     

24-hour blood pressure differences in hypertension and normotension in bed-confined subjects

This study investigates whether the degree of hypertension may be evaluated by information derived from the 24-h blood pressure (BP) curve unrelated to the pressure height. We performed 24-h BP intra-arterial monitoring in 52 bed-confined subjects (10 normotensives, 10 borderlines, and 32 hypertensives on WHO criteria). Computer analysis of 1152 BP values per subject per 24-h revealed the following: During the night hours, the percentage of the 1152 systolic BP values greater than or equal to 160 (in mmHg) increased (or did not change if 100%) in all subjects with mean 24-h systolic BP (24-h BP) greater than 170 and it decreased (or did not change if 0%) in all subjects with 24-h BP less than 150. The change in the percentage of the 1152 diastolic BP values greater than or equal to 95 during the night hours did not correlate to either the mean 24-h diastolic or systolic BP. The higher the mean 24-h systolic BP, the lower the skewness of the distribution of the 1152 systolic BP values (p less than 0.01). No such correlation existed between the skewness of the distribution of the 1152 diastolic BP values and either the mean 24-h diastolic or systolic BP. It is concluded that both the change in systolic BP during the night hours and the skewness of its distribution during the 24-h monitoring period are correlated to the severity of hypertension.     

X‐Chromosome Genetic Association Test Accounting for X‐Inactivation,Skewed X‐Inactivation,and Escape from X‐Inactivation

X‐chromosome inactivation (XCI) is the process in which one of the two copies of the X‐chromosome in females is randomly inactivated to achieve the dosage compensation of X‐linked genes between males and females. That is, 50% of the cells have one allele inactive and the other 50% of the cells have the other allele inactive. However, studies have shown that skewed or nonrandom XCI is a biological plausibility wherein more than 75% of cells have the same allele inactive. Also, some of the X‐chromosome genes escape XCI, i.e., both alleles are active in all cells. Current statistical tests for X‐chromosome association studies can either account for random XCI (e.g., Clayton's approach) or escape from XCI (e.g., PLINK software). Because the true XCI process is unknown and differs across different regions on the X‐chromosome, we proposed a unified approach of maximizing likelihood ratio over all biological possibilities: random XCI, skewed XCI, and escape from XCI. A permutation‐based procedure was developed to assess the significance of the approach. We conducted simulation studies to compare the performance of the proposed approach with Clayton's approach and PLINK regression. The results showed that the proposed approach has higher powers in the scenarios where XCI is skewed while losing some power in scenarios where XCI is random or XCI is escaped, with well‐controlled type I errors. We also applied the approach to the X‐chromosomal genetic association study of head and neck cancer.     

Comparison of two treatments with skewed ordinal responses

In clinical studies, the proportional odds model is widely used to compare treatment efficacies when the responses are categorically ordered. However, this model has been shown to be inappropriate when the proportional odds assumption is invalid, mainly because it is unable to control the type I error rate in such circumstances. To remedy this problem, the latent normal model was recently promoted and has been demonstrated to be superior to the proportional odds model. However, the application of the latent normal model is limited to compare treatments with similar underlying distributions except possibly their means and variances. When the underlying distributions are very different in skewness, both of the aforementioned procedures suffer from the undesirable inflation of the type I error rate. To solve the problem for clinical studies with ordinal responses, we provide a viable solution that relies on the use of the latent Weibull distribution, which is a member of the log‐location‐scale family. The proposed model is able to control the type I error rate regardless of the degree of skewness of the treatment responses. In addition, the power of the test also outperforms that of the latent normal model. The testing procedure draws on newly developed theoretical results related to latent distributions from the location‐scale family. The testing procedure is illustrated with two clinical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

A Comparative Study of Corrosion AA6061 and AlSi10Mg Alloys Produced by Extruded and Additive Manufacturing

The aim of this work was to evaluate the corrosion behavior of the AA6061 and AlSi10Mg alloys produced by extruded and additive manufacturing (selective laser melting, SLM). Alloys were immersed in two electrolytes in H₂O and 3.5 wt. % NaCl solutions at room temperature and their corrosion behavior was studied by electrochemical noise technique (EN). Three different methods filtered EN signals, and the statistical analysis was employed to obtain Rn, the localization index (LI), Kurtosis, skew, and the potential spectral density analysis (PSD). The Energy Dispersion Plots (EDP) of wavelets method was employed to determine the type of corrosion and the Hilbert–Huang Transform (HHT), analyzing the Hilbert Spectra. The result indicated that the amplitude of the transients in the time series in potential and current is greater in the AlSi10Mg alloy manufactured by additive manufacturing. The amplitude of the transients decreases in both alloys (AA6061 and AlSi10Mg) as time increases.