11,013 research outputs found
Multivariate Unified Skew-t Distributions And Their Properties
The unified skew-t (SUT) is a flexible parametric multivariate distribution
that accounts for skewness and heavy tails in the data. A few of its properties
can be found scattered in the literature or in a parameterization that does not
follow the original one for unified skew-normal (SUN) distributions, yet a
systematic study is lacking. In this work, explicit properties of the
multivariate SUT distribution are presented, such as its stochastic
representations, moments, SUN-scale mixture representation, linear
transformation, additivity, marginal distribution, canonical form, quadratic
form, conditional distribution, change of latent dimensions, Mardia measures of
multivariate skewness and kurtosis, and non-identifiability issue. These
results are given in a parametrization that reduces to the original SUN
distribution as a sub-model, hence facilitating the use of the SUT for
applications. Several models based on the SUT distribution are provided for
illustration
Some properties of the unified skew-normal distribution
For the family of multivariate probability distributions variously denoted as
unified skew-normal, closed skew-normal and other names, a number of properties
are already known, but many others are not, even some basic ones. The present
contribution aims at filling some of the missing gaps. Specifically, the
moments up to the fourth order are obtained, and from here the expressions of
the Mardia's measures of multivariate skewness and kurtosis. Other results
concern the property of log-concavity of the distribution, and closure with
respect to conditioning on intervals
Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution
The returns on most financial assets exhibit kurtosis and many also have probability distributions that possess skewness as well. In this paper a general multivariate model for the probability distribution of assets returns, which incorporates both kurtosis and skewness, is described. It is based on the multivariate extended skew-Student-t distribution. Salient features of the distribution are described and these are applied to the task of asset pricing. The paper shows that the market model is non-linear in general and that the sensitivity of asset returns to return on the market portfolio is not the same as the conventional beta, although this measure does arise in special cases. It is shown that the variance of asset returns is time varying and depends on the squared deviation of market portfolio return from its location parameter. The first order conditions for portfolio selection are described. Expected utility maximisers will select portfolios from an efficient surface, which is an analogue of the familiar mean-variance frontier, and which may be implemented using quadratic programming
Flexible modelling in statistics: past, present and future
In times where more and more data become available and where the data exhibit
rather complex structures (significant departure from symmetry, heavy or light
tails), flexible modelling has become an essential task for statisticians as
well as researchers and practitioners from domains such as economics, finance
or environmental sciences. This is reflected by the wealth of existing
proposals for flexible distributions; well-known examples are Azzalini's
skew-normal, Tukey's -and-, mixture and two-piece distributions, to cite
but these. My aim in the present paper is to provide an introduction to this
research field, intended to be useful both for novices and professionals of the
domain. After a description of the research stream itself, I will narrate the
gripping history of flexible modelling, starring emblematic heroes from the
past such as Edgeworth and Pearson, then depict three of the most used flexible
families of distributions, and finally provide an outlook on future flexible
modelling research by posing challenging open questions.Comment: 27 pages, 4 figure
An analysis of skewness and skewness persistence in three emerging markets
This paper reports an investigation into the extent and persistence of skewness in stock returns in three emerging markets, namely the Czech Republic, Kenya and Poland. The study is undertaken using the extended skew normal distribution and an asymmetric version of the generalised error distribution. The motivation for this paper is the hypothesis that skewness is a particular feature of returns in emerging markets; it may lack persistence and may decline in absolute terms as time passes and the market matures. When daily returns are considered, the majority of stocks in all three markets exhibit a significant degree of skewness. The value of the skewness parameter is often different in each of the three estimation periods considered. Little evidence has been found to support the view that skewness is an artifact of emerging or evolving markets. Over the period covered by the study, the number of stocks with a significant degree of skewness has remained more or less the same. For weekly returns, the same conclusions apply to the Czech Republic and to Kenya, but there is far less evidence of skewness in weekly returns on Polish Stocks. There is consistent evidence of short-term reversion in daily returns; increases (decreases) in mean return and volatility imply that there will be a decrease (increase) in skewness in the next month. This effect does not persist over longer time horizons
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