11,065 research outputs found
Additive versus multiplicative parameters - applications in economics and finance
In this paper, we pay our attention to geometric parameters and their
applications in economics and finance. We discuss the multiplicative models in
which a geometric mean and a geometric standard deviation are more natural than
arithmetic ones. We give two examples from Warsaw Stock Exchange in 1995--2009
and from a bid of 52-week treasury bills in 1992--2009 in Poland as an
illustrative example. For distributions having applications in finance and
insurance we give their multiplicative parameters as well as their estimations.
We consider, among others, heavy-tailed distributions such as lognormal and
Pareto distribution, applied to modelling of large losses
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 ïŹts to consecutive daily 2-year period returns of S&P500 index over [1950â2016], 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
Statistical Modeling of Spatial Extremes
The areal modeling of the extremes of a natural process such as rainfall or
temperature is important in environmental statistics; for example,
understanding extreme areal rainfall is crucial in flood protection. This
article reviews recent progress in the statistical modeling of spatial
extremes, starting with sketches of the necessary elements of extreme value
statistics and geostatistics. The main types of statistical models thus far
proposed, based on latent variables, on copulas and on spatial max-stable
processes, are described and then are compared by application to a data set on
rainfall in Switzerland. Whereas latent variable modeling allows a better fit
to marginal distributions, it fits the joint distributions of extremes poorly,
so appropriately-chosen copula or max-stable models seem essential for
successful spatial modeling of extremes.Comment: Published in at http://dx.doi.org/10.1214/11-STS376 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
A general framework for solving image inverse problems is introduced in this
paper. The approach is based on Gaussian mixture models, estimated via a
computationally efficient MAP-EM algorithm. A dual mathematical interpretation
of the proposed framework with structured sparse estimation is described, which
shows that the resulting piecewise linear estimate stabilizes the estimation
when compared to traditional sparse inverse problem techniques. This
interpretation also suggests an effective dictionary motivated initialization
for the MAP-EM algorithm. We demonstrate that in a number of image inverse
problems, including inpainting, zooming, and deblurring, the same algorithm
produces either equal, often significantly better, or very small margin worse
results than the best published ones, at a lower computational cost.Comment: 30 page
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