We extend the concept of distance correlation of Szekely, Rizzo and Bakirov (The Annals of Statistics, 2007) and propose the auto distance correlation function (ADCF) to measure the temporal dependence structure of time series. Unlike the classic measures of correlations such as the autocorrelation function, the proposed measure is zero if and only if the measured time series components are ind...

TES (Transform-Expand-Sample) is a versatile class of stochastic sequences which can capture arbitrary marginals and a wide variety of sample path behavior and autocorrelation functions. In TES, the initial variate is uniform on [0,1) and the next variate is obtained recursively by taking the fractional part (i.e., modulo-1 reduction) of a linear autoregressive scheme. We show how this class gi...

The series of acoustic emission events from loaded rock samples were studied by means of correlation analysis. As characteristic parameters of the correlation functions were chosen: the first values of the autocorrelation coefficients, the number of positive autocorrelation coefficients and the linearity of the autocorrelation function. The increase in the values of the autocorrelation coeffici...

We consider a particle immersed in a thermal reservoir and simultaneously subjected to an external random force that drives the system to a nonequilibrium situation. Starting from a Langevin equation description, we derive exact expressions for the mean-square displacement and the velocity autocorrelation function of the diffusing particle. An effective temperature is introduced to characterize...

We study the weak limit behaviour of the sample autocorrelation function (ACF) of non-linear stationary sequences with regularly varying nite-dimensional distributions. In particular, we consider the sample ACF of solutions to multivariate stochastic recurrence equations (SRE's). The latter includes the important class of the squares of GARCH processes. Point process convergence is exploited to...

Spatial structure of genetic variation within populations, an important interacting influence on evolutionary and ecological processes, can be analyzed in detail by using spatial autocorrelation statistics. This paper characterizes the statistical properties of spatial autocorrelation statistics in this context and develops estimators of gene dispersal based on data on standing patterns of gene...

We study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits. We obtain an expansion of the autocorrelation function in terms of the correlation length. For localized states, like bouncing ball modes or states living on tori, a simple model using only classical input gives good agreement with the exact res...

The three-state agent-based 2D model of nancial markets in the version proposed by Giulia Iori in 2002 has been herein extended. We have introduced the increase of herding behaviour by modelling the altering trust of an agent in his nearest neighbours. The trust increases if the neighbour has foreseen the price change correctly and the trust decreases in the opposite case. Our version only slig...