Related papers: Self-affinity in financial asset returns
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…
Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that…
Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the…
The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments.…
Many financial and economic variables, including financial returns, exhibit nonlinear dependence, heterogeneity and heavy-tailedness. These properties may make problematic the analysis of (non-)efficiency and volatility clustering in…
In this paper we present a method to generate independent samples for a general random variable, either continuous or discrete. The algorithm is an extension of the acceptance-rejection method, and it is particularly useful for kinetic…
Fluctuation relations are powerful equalities that hold far from equilibrium. However, the standard approach to include measurement and feedback schemes may become inapplicable in certain situations, including continuous measurements,…
The aim of this paper is first the detection of multiple abrupt changes of the long-range dependence (respectively self-similarity, local fractality) parameters from a sample of a Gaussian stationary times series (respectively time series,…
The response of thermodynamic systems perturbed out of an equilibrium steady-state is described by the reciprocal and the fluctuation-dissipation relations. The so-called fluctuation theorems extended the study of fluctuations far beyond…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
We explore a decomposition in which returns on a large class of portfolios relative to the market depend on a smooth non-negative drift and changes in the asset price distribution. This decomposition is obtained using general continuous…
It will be discussed the statistics of the extreme values in time series characterized by finite-term correlations with non-exponential decay. Precisely, it will be considered the results of numerical analyses concerning the return…
The ordinary Levy motion is a random process whose stationary independent increments are statistically self-affine and distributed with a stable probability law characterized by the Levy index alpha, 0 < alpha < 2. The divergence of…
We introduce a new approach to financial returns based on an infinite family of statistics called slide statistics. The evidence these statistics provide suggests that certain distributions such as the stable distributions are not good…
The self-affine analysis and erraticity analysis of pseudorapidity gaps are performed for the data of 400GeV/$c$ pp collisions. The self-affine analysis has been shown to exhibit a better scaling behavior. The self-affine multifractal…
A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the…
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…
We propose a framework combining detrended fluctuation analysis with standard regression methodology. The method is built on detrended variances and covariances and it is designed to estimate regression parameters at different scales and…
We discuss the foundations of factor or regression models in the light of the self-consistency condition that the market portfolio (and more generally the risk factors) is (are) constituted of the assets whose returns it is (they are)…
In this paper we propose a new model for volatility fluctuations in financial time series. This model relies on a non-stationary gaussian process that exhibits aging behavior. It turns out that its properties, over any finite time interval,…