# Estimating the spectral measure of a multivariate stable distribution via spherical harmonic analysis

## Author

Listed:
• Pivato, Marcus
• Seco, Luis

## Abstract

A new method is developed for estimating the spectral measure of a multivariate stable probability measure, by representing the measure as a sum of spherical harmonics.

## Suggested Citation

• Pivato, Marcus & Seco, Luis, 2003. "Estimating the spectral measure of a multivariate stable distribution via spherical harmonic analysis," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 219-240, November.
• Handle: RePEc:eee:jmvana:v:87:y:2003:i:2:p:219-240
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File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(03)00052-6

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## References listed on IDEAS

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1. B. N. Cheng & S. T. Rachev, 1995. "Multivariate Stable Futures Prices," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 133-153.
2. Press, S. J., 1972. "Multivariate stable distributions," Journal of Multivariate Analysis, Elsevier, vol. 2(4), pages 444-462, December.
3. Samuelson, Paul A., 1967. "Efficient Portfolio Selection for Pareto-Lévy Investments," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(02), pages 107-122, June.
4. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
5. Bawa, Vijay S & Elton, Edwin J & Gruber, Martin J, 1979. "Simple Rules for Optimal Portfolio Selection in Stable Paretian Markets," Journal of Finance, American Finance Association, vol. 34(4), pages 1041-1047, September.
6. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
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## Citations

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Cited by:

1. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
2. Mohammad Mohammadi & Adel Mohammadpour & Hiroaki Ogata, 2015. "On estimating the tail index and the spectral measure of multivariate $$\alpha$$ α -stable distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 549-561, July.
3. Molchanov, Ilya, 2009. "Convex and star-shaped sets associated with multivariate stable distributions, I: Moments and densities," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2195-2213, November.
4. Matsui, Muneya & Takemura, Akimichi, 2009. "Integral representations of one-dimensional projections for multivariate stable densities," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 334-344, March.
5. Buckley, Ian & Saunders, David & Seco, Luis, 2008. "Portfolio optimization when asset returns have the Gaussian mixture distribution," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1434-1461, March.
6. Ogata, Hiroaki, 2013. "Estimation for multivariate stable distributions with generalized empirical likelihood," Journal of Econometrics, Elsevier, vol. 172(2), pages 248-254.
7. Lombardi, Marco J. & Veredas, David, 2009. "Indirect estimation of elliptical stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2309-2324, April.

### Keywords

Stable probability distributions Infinitely divisible distributions Spectral measure Parameter estimation Spherical harmonics;

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