Related papers: Slide Statistics And Financial Returns
In this paper we introduce a new type of pattern -- a flipping correlation pattern. The flipping patterns are obtained from contrasting the correlations between items at different levels of abstraction. They represent surprising…
An increase in the novelty of news predicts negative stock market returns and negative macroeconomic outcomes over the next year. We quantify news novelty - changes in the distribution of news text - through an entropy measure, calculated…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
We consider a random walk of $n$ steps starting at $x_0=0$ with a double exponential (Laplace) jump distribution. We compute exactly the distribution $p_{k,n}(\Delta)$ of the gap $d_{k,n}$ between the $k^{\rm th}$ and $(k+1)^{\rm th}$…
Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the…
We consider a formal discretisation of Euclidean quantum gravity defined by a statistical model of random $3$-regular graphs and making using of the Ollivier curvature, a coarse analogue of the Ricci curvature. Numerical analysis shows that…
The time series theory is set in this work under the domain of general elliptically contoured distributions. The advent of a time series approach that is in accordance with the expected reality of dependence between errors, transfers the…
We define a general notion of entropy in elementary, algebraic terms. Based on that, weak forms of a scalar product and a distance measure are derived. We give basic properties of these quantities, generalize the Cauchy-Schwarz inequality,…
A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the…
I present a novel mathematical technique for dealing with the infinities arising from divergent sums and integrals. It assigns them fine-grained infinite values from the set of hyperreal numbers in a manner that refines the standard…
We propose a family of "exactly solvable" probability distributions to approximate partition functions of two-dimensional statistical mechanics models. While these distributions lie strictly outside the mean-field framework, their free…
A major issue in financial economics is the behavior of asset returns over long horizons. Various estimators of long range dependence have been proposed. Even though some have known asymptotic properties, it is important to test their…
We introduce a new family of shift spaces --- the subordinate shifts. Using subordinate shifts we prove in an elementary way that for every nonnegative real number $t$ there is a shift space with entropy $t$.
This paper studies statistics of riffle shuffles by relating them to random word statistics with the use of inverse shuffles. Asymptotic normality of the number of descents and inversions in riffle shuffles with convergence rates of order…
A fundamental problem of statistical data analysis, distribution density estimation by experimental data, is considered. A new method with optimal asymptotic behavior, the root density estimator, is developed. The method proposed may be…
The basic notions of statistical mechanics (microstates, multiplicities) are quite simple, but understanding how the second law arises from these ideas requires working with cumbersomely large numbers. To avoid getting bogged down in…
A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be…
Superpositions of different statistics on different time or spatial scales (in short, superstatistics) can naturally lead to an effective description by nonextensive statistical mechanics. We first discuss the role of escort distributions…
Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann- Gibbs form of the entropy ensures that…
Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played by quantities such as various order parameters,…