78,674 research outputs found
MaxSkew and MultiSkew: Two R Packages for Detecting, Measuring and Removing Multivariate Skewness
Skewness plays a relevant role in several multivariate statistical
techniques. Sometimes it is used to recover data features, as in cluster
analysis. In other circumstances, skewness impairs the performances of
statistical methods, as in the Hotelling's one-sample test. In both cases,
there is the need to check the symmetry of the underlying distribution, either
by visual inspection or by formal testing. The R packages MaxSkew and MultiSkew
address these issues by measuring, testing and removing skewness from
multivariate data. Skewness is assessed by the third multivariate cumulant and
its functions. The hypothesis of symmetry is tested either nonparametrically,
with the bootstrap, or parametrically, under the normality assumption. Skewness
is removed or at least alleviated by projecting the data onto appropriate
linear subspaces. Usages of MaxSkew and MultiSkew are illustrated with the Iris
dataset
Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. Open accessThis paper reports a new methodology and results on the forecast of the numerical value of the fat tail(s) in asset returns distributions using the irrational fractional Brownian motion model. Optimal model parameter values are obtained from fits to consecutive daily 2-year period returns of S&P500 index over [1950–2016], generating 33-time series estimations. Through an econometric model,the kurtosis of returns distributions is modelled as a function of these parameters. Subsequently an auto-regressive analysis on these parameters advances the modelling and forecasting of kurtosis and returns distributions, providing the accurate shape of returns distributions and measurement of Value at Risk
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
Bayesian modelling of skewness and kurtosis with two-piece scale and shape distributions
We formalise and generalise the definition of the family of univariate double
two--piece distributions, obtained by using a density--based transformation of
unimodal symmetric continuous distributions with a shape parameter. The
resulting distributions contain five interpretable parameters that control the
mode, as well as the scale and shape in each direction. Four-parameter
subfamilies of this class of distributions that capture different types of
asymmetry are discussed. We propose interpretable scale and location-invariant
benchmark priors and derive conditions for the propriety of the corresponding
posterior distribution. The prior structures used allow for meaningful
comparisons through Bayes factors within flexible families of distributions.
These distributions are applied to data from finance, internet traffic and
medicine, comparing them with appropriate competitors
Skewed superstatistical distributions from a Langevin and Fokker-Planck approach
The superstatistics concept is a useful statistical method to describe
inhomogeneous complex systems for which a system parameter fluctuates
on a large spatio-temporal scale. In this paper we analyze a measured time
series of wind speed fluctuations and extract the superstatistical distribution
function directly from the data. We construct suitable Langevin and
Fokker-Planck models with a position dependent -field and show that they
reduce to standard type of superstatistics in the overdamped limit.Comment: 7 pages, 6 figure
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