| Authors: |
I.M. Gleria
and A.D. Figueiredo
and S. Dasilva
and R. Matsushita
|
| Editors: |
Luciano Pietronero
and Vittorio Loreto
and Stefano Zapperi
|
| URL: |
http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=52 |
| Tags: |
convergence
correlations
econophysics
exchange
foreign
laws
nonlinear
power
rates
slow
statphys23
topic-11
|
| Abstract: |
In recent papers we have shown that the sluggish convergence of truncated L\' evy flights [1] to the Gaussian distribution and the presence of scaling power laws in their probability of return to the origin can be explained by autocorrelation in data [2,3]. Here we enlarge the scope of our results considering the
role of generalized nonlinear correlations. The role of the correlations in the convergence process as well as the problem of establishing the distance of a given distribution to the Gaussian are analyzed in detail. We show that whereas power laws in the second moment can still be explained by linear correlation of pairs, slow convergence emerge from nonlinear correlations.
Our approach is exemplified with data from foreign exchange rate [4,5].\\
1) R.N. Mantegna, H.E. Stanley, {\it Stochastic process with ultraslow convergence to a Gaussian: the truncated Levy flight}, Phys. Rev. Lett. {\bf 73} (1994) 2946-2949.\\
2) A. Figueiredo, I. Gleria, R. Matsushita, S. Da Silva, {\it Autocorrelation as a source of truncated Levy flights in foreign exchange rates}, Physica A {\bf 323} (2003), 601-625.\\
3) A. Figueiredo, I. Gleria, R. Matsushita, S. Da Silva, {\it On the origins of truncated Levy flights}, Phys. Lett. A {\bf 315} (2003) 51-60.\\
4) I. Gleria, A. Figueiredo, R. Matsushita, S. Da Silva, {\it Levy flights,
autocorrelation ans slow convergente}, Physica A {\bf 337} (2004), 369-383.\\
5) S. Da Silva,R. Matsushita, I. Gleria, A. Figueiredo, P. Rathie, {\it International finance, Levy distributions, and the econophysics of
exchange rates}, Communications in Nonlinear Science and Numerical Simulations {\bf 10} (2005), 365-393. |
@incollection{statphys23_0052,
title = {Nonlinear correlations, power laws and slow convergence to the gaussian},
address = {Genova, Italy},
author = {I.M. Gleria and A.D. Figueiredo and S. Dasilva and R. Matsushita},
booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
month = {9-13 July},
url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=52},
year = {2007},
abstract = {In recent papers we have shown that the sluggish convergence of truncated L\' evy flights [1] to the Gaussian distribution and the presence of scaling power laws in their probability of return to the origin can be explained by autocorrelation in data [2,3]. Here we enlarge the scope of our results considering the
role of generalized nonlinear correlations. The role of the correlations in the convergence process as well as the problem of establishing the distance of a given distribution to the Gaussian are analyzed in detail. We show that whereas power laws in the second moment can still be explained by linear correlation of pairs, slow convergence emerge from nonlinear correlations.
Our approach is exemplified with data from foreign exchange rate [4,5].\\
1) R.N. Mantegna, H.E. Stanley, {\it Stochastic process with ultraslow convergence to a Gaussian: the truncated Levy flight}, Phys. Rev. Lett. {\bf 73} (1994) 2946-2949.\\
2) A. Figueiredo, I. Gleria, R. Matsushita, S. Da Silva, {\it Autocorrelation as a source of truncated Levy flights in foreign exchange rates}, Physica A {\bf 323} (2003), 601-625.\\
3) A. Figueiredo, I. Gleria, R. Matsushita, S. Da Silva, {\it On the origins of truncated Levy flights}, Phys. Lett. A {\bf 315} (2003) 51-60.\\
4) I. Gleria, A. Figueiredo, R. Matsushita, S. Da Silva, {\it Levy flights,
autocorrelation ans slow convergente}, Physica A {\bf 337} (2004), 369-383.\\
5) S. Da Silva,R. Matsushita, I. Gleria, A. Figueiredo, P. Rathie, {\it International finance, Levy distributions, and the econophysics of
exchange rates}, Communications in Nonlinear Science and Numerical Simulations {\bf 10} (2005), 365-393.},
keywords = {convergence correlations econophysics exchange foreign laws nonlinear power rates slow statphys23 topic-11 }
}
::