Fitting asset returns to skewed distributions: Are the skew-normal and skew-student good models?

2014 ◽  
Vol 59 ◽  
pp. 45-56 ◽  
Author(s):  
Martin Eling
Keyword(s):  
Asset Returns ◽  
Skewed Distributions ◽  
Skew Normal

scholarly journals Likelihood Inference of Nonlinear Models Based on a Class of Flexible Skewed Distributions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xuedong Chen ◽  
Qianying Zeng ◽  
Qiankun Song
Keyword(s):  
Nonlinear Models ◽  
Profile Likelihood ◽  
Hypothesis Test ◽  
Likelihood Inference ◽  
Maximum Likelihood Estimates ◽  
Skewed Distributions ◽  
Confidence Estimation ◽  
Nonlinear Regression Models ◽  
Newton Raphson ◽  
Skew Normal

This paper deals with the issue of the likelihood inference for nonlinear models with a flexible skew-t-normal (FSTN) distribution, which is proposed within a general framework of flexible skew-symmetric (FSS) distributions by combining with skew-t-normal (STN) distribution. In comparison with the common skewed distributions such as skew normal (SN), and skew-t (ST) as well as scale mixtures of skew normal (SMSN), the FSTN distribution can accommodate more flexibility and robustness in the presence of skewed, heavy-tailed, especially multimodal outcomes. However, for this distribution, a usual approach of maximum likelihood estimates based on EM algorithm becomes unavailable and an alternative way is to return to the original Newton-Raphson type method. In order to improve the estimation as well as the way for confidence estimation and hypothesis test for the parameters of interest, a modified Newton-Raphson iterative algorithm is presented in this paper, based on profile likelihood for nonlinear regression models with FSTN distribution, and, then, the confidence interval and hypothesis test are also developed. Furthermore, a real example and simulation are conducted to demonstrate the usefulness and the superiority of our approach.

scholarly journals A regime switching skew-normal model of contagion

2018 ◽  
Vol 23 (1) ◽  
Author(s):  
Joshua C.C. Chan ◽  
Renée A. Fry-McKibbin ◽  
Cody Yu-Ling Hsiao
Keyword(s):  
Regime Switching ◽  
Global Financial Crisis ◽  
Asset Returns ◽  
Time Varying ◽  
Skew Normal Distribution ◽  
The Us ◽  
Market Contagion ◽  
The Global Financial Crisis ◽  
European Equity ◽  
Skew Normal

Abstract A flexible multivariate model of a time-varying joint distribution of asset returns is developed which allows for regime switching and a joint skew-normal distribution. A suite of tests for linear and nonlinear financial market contagion is developed within the framework. The model is illustrated through an application to contagion between US and European equity markets during the Global Financial Crisis. The results show that correlation contagion dominates coskewness contagion, but that coskewness contagion is significant for Greece. A flight to safety to the US is also evident in the significance of breaks in the skewness parameter in the crisis regime. Comparison to the Asian crisis shows that similar patterns emerge, with a flight to safety to Japan, and Malaysia affected by coskewnes contagion with Hong Kong.

scholarly journals Skewed and Flexible Skewed Distributions: A Modern Look at the Distribution of BMI

2017 ◽  
Vol 14 (2) ◽  
Author(s):  
Thao Tran ◽  
Cara Wiskow ◽  
Mohammad Aziz
Keyword(s):  
Body Mass Index ◽  
Normal Distribution ◽  
Body Mass ◽  
Model Parameters ◽  
Skew Normal Distribution ◽  
Scale Mixture ◽  
Skewed Distributions ◽  
Goodness Of Fit Test ◽  
T Distribution ◽  
Skew Normal

The purpose of this study is to find distributions that best model body mass index (BMI) data. BMI has become a standard health indicator and numerous studies have been done to examine the distribution of BMI. Due to the skew and bimodal nature, we focus on modeling BMI with flexible skewed distributions. The distributions are fitted to University of Wisconsin–Eau Claire (UWEC) BMI data and to a data obtained from National Health and Nutrition Survey (NHANES). The model parameters are obtained using maximum likelihood estimation method. We compare flexible models to more conventional distributions, such as skew-normal, and skew-t distributions using AIC and BIC and Kolmogorov-Smirnov (K-S) goodness-of-fit test. Our results indicate that the skew-t and Alpha-Skew-Laplace distributions are reasonably competitive when describing unimodal BMI data whereas Alpha-Skew-Laplace and finite mixture of scale mixture of skew-normal and skew-t distributions are better alternatives to both unimodal and bimodal conventional distributions. The results we obtained are useful because we believe the models discussed in ours study will offer a framework for testing features such as bimodality, asymmetry, and robustness of the BMI data, thus providing a more detailed and accurate understanding of the distribution of BMI. KEYWORDS: Body Mass Index; Skew-normal distribution; Skew-t distribution; Flexible skewed distributions; Mixture distributions; Scale mixture of skew-normal distribution; K-S test

The Skew-Normal and Related Families

2009 ◽  
Author(s):  
Adelchi Azzalini ◽  
Antonella Capitanio
Keyword(s):  
Skew Normal

Properties of the beta coefficient of the global minimum variance portfolio

2020 ◽  
Vol 8 (1) ◽  
pp. 11-21
Author(s):  
S. M. Yaroshko ◽  
◽  
M. V. Zabolotskyy ◽  
T. M. Zabolotskyy ◽  
◽  
...  
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Global Minimum ◽  
Asset Returns ◽  
Minimum Variance ◽  
Benchmark Portfolio ◽  
Beta Coefficient ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio ◽  
Daily Returns

The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.

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