An exact solution is presented to a model that mimics the crowding effect in financial markets which arises when groups of agents share information. We show that the size distribution of groups of agents has a power law tail with an exponential cut-off. As the size of these groups determines the supply and demand balance, this implies heavy tails in the distribution of price variation. The mome...

In this paper we study the properties of a kurtosis matrix and propose its eigenvectors as interesting directions to reveal the possible cluster structure of a data set. Under a mixture of elliptical distributions with proportional scatter matrix, it is shown that a subset of the eigenvectors of the fourth-ordermomentmatrix corresponds to Fisher’s linear discriminant subspace. The eigenvectors ...

In blind extraction of independent sources, the normalised Kurtosis is a normally used cost function for the cases without the initial prewhitening. The applications of this method are, however, limited to noise-free mixtures, which is not realistic. We therefore address this issue and propose a new cost function based on the normalised Kurtosis, which makes this class of algorithms suitable fo...

Abstract: This paper carries out an investigation of the orthogonal-polynomial approach to reshaping symmetric distributions to fit in with data requirements so as to cover the multivariate case. With this objective in mind, reference is made to the class of spherical distributions, given that they provide a natural multivariate generalization of univariate even densities. After showing how to ...

In this paper, a new analytical approximated expression for the sharpness parameter of a Generalised Gaussian pdf model as a function of a higher-order statistic, namely normalised kurtosis is proposed. The approximation is based on some mathematical considerations concerning the Gamma function, and provides a very precise sharpness evaluation for a wide range of normalised kurtosis values. As ...

Recent studies of high quality, high resolution traffic measurements have revealed that network traffic appears to be statistically self similar. Contrary to the common belief, aggregating self-similar traffic streams can actually intensify rather than diminish burstiness. Thus, traffic prediction plays an important role in network management. In this paper, Least Mean Kurtosis (LMK), which use...

In spite of their importance, third or higher moments of portfolio returns are often neglected in portfolio construction problems due to the computational difficulties associated with them. In this paper, we propose a new robust mean–variance approach that can control portfolio skewness and kurtosis without imposing higher moment terms. The key idea is that, if the uncertainty sets are properly...

ABSTRACT This paper analyzes a pentanomial lattice model for option pricing that incorporates skewness and kurtosis of the underlying asset. The lattice is constructed using a moment matching procedure, and explicit positivity conditions for branch probabilities are provided in terms of skewness and kurtosis. We also explore the limiting distribution of this lattice, which is compound Poisson, ...

This paper deals with the optimization of kurtosis for complex-valued signals in the independent component analysis (ICA) framework, where source signals are linearly and instantaneously mixed. Inspired by the recently proposed reference-based contrast schemes, a similar contrast function is put forward, based on which a new fast fixed-point (FastICA) algorithm is proposed. The new optimization...

In this paper, we consider spectrum sensing in cognitive radio networks based on higher order statistics. The kurtosis, a fourth order statistic, which is a measure of deviation from Gaussianity, is used as a detection statistic. An optimum threshold is set up based on the Neyman-Pearson criterion and analytical expression for upper bound on probability of miss is derived for a single pair of p...