Related papers: Slide Statistics And Financial Returns
We associate with any finite subset of a metric space an infinite sequence of scale invariant numbers $\rho_1,\rho_2,\dots$ derived from a variant of differential entropy called the genial entropy. As statistics for point processes, these…
We introduce a family of scale-invariant entropy statistics derived from logarithmically aggregated distance distributions of point processes, with prime numbers serving as a motivating example. The construction associates to each finite…
We test for departures from normal and independent and identically distributed (NIID) returns, when returns under the alternative hypothesis are self-affine. Self-affine returns are either fractionally integrated and long-range dependent,…
Inverse statistics in economics is considered. We argue that the natural candidate for such statistics is the investment horizons distribution. This distribution of waiting times needed to achieve a predefined level of return is obtained…
We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
Sliced inverse regression is one of the most popular sufficient dimension reduction methods. Originally, it was designed for independent and identically distributed data and recently extend to the case of serially and spatially dependent…
Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $\beta$, so that the probability distribution is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta$,…
Entropic dynamics is a framework for defining dynamical systems that is aligned with the principles of information theory. In an entropic dynamics model for motion on a statistical manifold, we find that the rate of changes for expected…
For a family of stochastic differential equations, we investigate the asymptotic behaviors of its corresponding Picard's iteration, establishing convergence results in terms of relative entropy. Our convergence results complement the…
In this study an attempt has been made to propose a way to develop new distribution. For this purpose, we need only idea about distribution function. Some important statistical properties of the new distribution like moments, cumulants,…
Stochastic differential equations have been an important tool in modeling complex financial relations, equipped with the possibility of being multidimensional to better oversee complexities inherent in finance. This multidimensionality,…
Large entropy fluctuations in an equilibrium steady state of classical mechanics were studied in extensive numerical experiments on a simple 2--freedom strongly chaotic Hamiltonian model described by the modified Arnold cat map. The rise…
This paper deals with tail diversification in financial time series through the concept of statistical independence by way of differential entropy and mutual information. By using moments as contrast functions to isolate the tails of the…
We derive Bose-Einstein statistics and Fermi-Dirac statistics by Principle of Maximum Entropy applied to two families of entropy functions different from the Boltzmann-Gibbs-Shannon entropy. These entropy functions are identified with…
We present a symmetry analysis of the distribution of variations of different financial indices, by means of a statistical procedure developed by the authors based on a symmetry statistic by Einmahl and Mckeague. We applied this statistical…
The problem of inverse statistics (statistics of distances for which the signal fluctuations are larger than a certain threshold) in differentiable signals with power law spectrum, $E(k) \sim k^{-\alpha}$, $3 \le \alpha < 5$, is discussed.…
The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…
The question of deriving general force/flux relationships that apply out of the linear response regime is a central topic of theories for nonequilibrium statistical mechanics. This work applies an information theory perspective to compute…
We propose skewed stable random projections for approximating the pth frequency moments of dynamic data streams (0<p<=2), which has been frequently studied in theoretical computer science and database communities. Our method significantly…