Estimation of α-Stable Sub-Gaussian Distributions for Asset Returns

Part of the Contributions to Economics book series (CE)

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.


Random Vector Asset Return Stable Distribution Tail Dependence Tail Index 


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© Physica-Verlag Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Econometrics Statistics and Mathematical FinanceUniversity of KarlsruheGermany
  2. 2.Yale School of ManagementNew Haven CTUSA

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