@inproceedings{7749c97469e843faacb722ec0e556ed4,

title = "Estimation of α-stable sub-Gaussian distributions for asset returns",

abstract = "Fitting multivariate α-stable distributions to data is still not feasible in higher dimensions since the (non-parametric) spectral measure of the characteristic function is extremely difficult to estimate in dimensions higher than 2. This was shown by [3] and [15]. α-stable sub-Gaussian distributions are a particular (parametric) subclass of the multivariate α-stable distributions. We present and extend a method based on [16] to estimate the dispersion matrix of an α-stable sub-Gaussian distribution and estimate the tail index α of the dis-tribution. In particular, we develop an estimator for the off-diagonal entries of the dispersion matrix that has statistical properties superior to the normal off-diagonal estimator based on the covariation. Furthermore, this approach allows estimation of the dispersion matrix of any normal variance mixture distribution up to a scale parameter. We demonstrate the behaviour of these estimators by fitting an α-stable sub-Gaussian distribution to the DAX30 components. Finally, we conduct a stable principal component analysis and calculate the coefficient of tail dependence of the prinipal components.",

author = "Sebastian Kring and Rachev, {Svetlozar T.} and Markus H{\"o}chst{\"o}tter and Fabozzi, {Frank J.}",

year = "2009",

doi = "10.1007/978-3-7908-2050-8-6",

language = "English",

isbn = "9783790820492",

series = "Contributions to Economics",

pages = "111--152",

editor = "Georg Bol and Svetlozar Rachev and Reinhold Wurth",

booktitle = "Risk Assessment",

}