arXiv subjects

Sergio Arianos

Publications and source records attributed to Sergio Arianos.

3 recordsLinked to original sources

arXiv2009

Cross-correlation of long-range correlated series

A method for estimating the cross-correlation $C_{xy}(τ)$ of long-range correlated series $x(t)$ and $y(t)$, at varying lags $τ$ and scales $n$, is proposed. For fractional Brownian motions with Hurst exponents $H_1$ and $H_2$, the asymptotic expression of $C_{xy}(τ)$ depends only on the lag $τ$ (wide-sense stationarity) and scales as a power of $n$ with exponent ${H_1+H_2}$ for $τ\to 0$. The method is illustrated on (i) financial series, to show the leverage effect; (ii) genomic sequences, to estimate the correlations between structural parameters along the chromosomes.

q-fin.ST↗

arXiv2008

Matrix formulation of superspace on 1D lattice with two supercharges

Following the approach developed by some of the authors in recent papers and using a matrix representation for the superfields, we formulate an exact supersymmetric theory with two supercharges on a one dimensional lattice. In the superfield formalism supersymmetry transformations are uniquely defined and do not suffer of the ambiguities recently pointed out by some authors. The action can be written in a unique way and it is invariant under all supercharges. A modified Leibniz rule applies when supercharges act on a superfield product and the corresponding Ward identities take a modified form but hold exactly at least at the tree level, while their validity in presence of radiative corrections is still an open problem and is not considered here.

hep-lat↗

arXiv2006

Detrending Moving Average variance: a derivation of the scaling law

The Hurst exponent $H$ of long range correlated series can be estimated by means of the Detrending Moving Average (DMA) method. A computational tool defined within the algorithm is the generalized variance $ σ_{DMA}^2={1}/{(N-n)}\sum_i [y(i)-\widetilde{y}_n(i)]^2\:$, with $\widetilde{y}_n(i)= {1}/{n}\sum_{k}y(i-k)$ the moving average, $n$ the moving average window and $N$ the dimension of the stochastic series $y(i)$. This ability relies on the property of $σ_{DMA}^2$ to scale as $n^{2H}$. Here, we analytically show that $σ_{DMA}^2$ is equivalent to $C_H n^{2H}$ for $n\gg 1$ and provide an explicit expression for $C_H$.

physics.data-an↗