We introduce a new measure of dependence between the components of a symmetric α-stable random vector that we call the signed symmetric covariation coefficient. We show that this coefficient satisfies the properties of the classical Pearson coefficient. Moreover, we show that in the case of sub-Gaussian random vectors, this coefficient coincide with the association parameter and the generalized association parameter.
On introduit ici une nouvelle mesure de dépendance entre les composantes d'un vecteur aléatoire α-stable symétrique appelé coefficient de covariation symétrique signé. On montre que ce coefficient satisfait les propriétés du coefficient de corrélation classique. De plus, on montre que dans le cas des vecteurs alétoires sous-gaussiens, ce coefficient coïncide avec le paramètre d'association et la version généralisée de ce paramètre appelée gap.
Accepted:
Published online:
@article{CRMATH_2009__347_5-6_315_0,
author = {Garel, Bernard and Kodia, Bern\'edy},
title = {Signed symmetric covariation coefficient for alpha-stable dependence modeling},
journal = {Comptes Rendus. Math\'ematique},
pages = {315--320},
publisher = {Elsevier},
volume = {347},
number = {5-6},
year = {2009},
doi = {10.1016/j.crma.2009.01.013},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.01.013/}
}
TY - JOUR AU - Garel, Bernard AU - Kodia, Bernédy TI - Signed symmetric covariation coefficient for alpha-stable dependence modeling JO - Comptes Rendus. Mathématique PY - 2009 SP - 315 EP - 320 VL - 347 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.01.013/ DO - 10.1016/j.crma.2009.01.013 LA - en ID - CRMATH_2009__347_5-6_315_0 ER -
%0 Journal Article %A Garel, Bernard %A Kodia, Bernédy %T Signed symmetric covariation coefficient for alpha-stable dependence modeling %J Comptes Rendus. Mathématique %D 2009 %P 315-320 %V 347 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.01.013/ %R 10.1016/j.crma.2009.01.013 %G en %F CRMATH_2009__347_5-6_315_0
Garel, Bernard; Kodia, Bernédy. Signed symmetric covariation coefficient for alpha-stable dependence modeling. Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 315-320. doi : 10.1016/j.crma.2009.01.013. http://www.numdam.org/articles/10.1016/j.crma.2009.01.013/
[1] Linear problems in pth order and stable processes, SIAM Journal on Applied Mathematics, Volume 41 (1981) no. 2, pp. 43-69
[2] L. d'Estampes, Traitement statistique des processus alpha-stables : mesures de dépendance et identification des AR stables. Tests séquentiels tronqués. Thèse, Institut National Polytechnique de Toulouse, 2003
[3] Revealing some unexpected dependence properties of linear combinations of stable random variables using symmetric covariation, Communications in Statistics: Theory and Methods, Volume 33 (2004) no. 4, pp. 769-786
[4] Regression and autoregression with infinite variance, Advanced Applied Probabilities, Volume 6 (1974), pp. 768-783
[5] Properties of certain symmetric stable distributions, Journal of Multivariate Analysis, Volume 8 (1978) no. 3, pp. 346-360
[6] Multivariate stable distributions, Journal of Multivariate Analysis, Volume 2 (1972), pp. 444-462
[7] Some remarks on multivariate stable distributions, Journal of Multivariate Analysis, Volume 6 (1976), pp. 356-368
[8] Stable Non-Gaussian Random Processes, Stochastic Modeling, Chapman & Hall, New York–London, 1994
[9] Chance and Stability, Stable Distributions and Their Applications, de Gruyter, Berlin, New York, 1999
Cited by Sources:
