4,343 research outputs found
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
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
A multivariate generalized independent factor GARCH model with an application to financial stock returns
We propose a new multivariate factor GARCH model, the GICA-GARCH model ,
where the data are assumed to be generated by a set of independent components (ICs).
This model applies independent component analysis (ICA) to search the conditionally
heteroskedastic latent factors. We will use two ICA approaches to estimate the ICs. The
first one estimates the components maximizing their non-gaussianity, and the second
one exploits the temporal structure of the data. After estimating the ICs, we fit an
univariate GARCH model to the volatility of each IC. Thus, the GICA-GARCH reduces
the complexity to estimate a multivariate GARCH model by transforming it into a small
number of univariate volatility models. We report some simulation experiments to show
the ability of ICA to discover leading factors in a multivariate vector of financial data.
An empirical application to the Madrid stock market will be presented, where we
compare the forecasting accuracy of the GICA-GARCH model versus the orthogonal
GARCH one
On the interplay between multiscaling and stocks dependence
We find a nonlinear dependence between an indicator of the degree of
multiscaling of log-price time series of a stock and the average correlation of
the stock with respect to the other stocks traded in the same market. This
result is a robust stylized fact holding for different financial markets. We
investigate this result conditional on the stocks' capitalization and on the
kurtosis of stocks' log-returns in order to search for possible confounding
effects. We show that a linear dependence with the logarithm of the
capitalization and the logarithm of kurtosis does not explain the observed
stylized fact, which we interpret as being originated from a deeper
relationship.Comment: 19 pages, 8 figures, 9 table
Fourth Moments and Independent Component Analysis
In independent component analysis it is assumed that the components of the
observed random vector are linear combinations of latent independent random
variables, and the aim is then to find an estimate for a transformation matrix
back to these independent components. In the engineering literature, there are
several traditional estimation procedures based on the use of fourth moments,
such as FOBI (fourth order blind identification), JADE (joint approximate
diagonalization of eigenmatrices), and FastICA, but the statistical properties
of these estimates are not well known. In this paper various independent
component functionals based on the fourth moments are discussed in detail,
starting with the corresponding optimization problems, deriving the estimating
equations and estimation algorithms, and finding asymptotic statistical
properties of the estimates. Comparisons of the asymptotic variances of the
estimates in wide independent component models show that in most cases JADE and
the symmetric version of FastICA perform better than their competitors.Comment: Published at http://dx.doi.org/10.1214/15-STS520 in the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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