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Estimating multivariate heavy tails and principal directions easily, with an application to international exchange rates

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  • Tsionas, Efthymios G.

Abstract

In this paper, we consider the estimation of the tail indices of distributions in the domain of attraction of stable laws. We follow the approach of Meerschaert and Scheffler (1999), which requires exclusively the spectral decomposition of the uncentered sample moment matrix containing the moments of a collection of time series. The technique is applied successfully to ten major currencies, using daily data over the period 1996–2012.

Suggested Citation

  • Tsionas, Efthymios G., 2012. "Estimating multivariate heavy tails and principal directions easily, with an application to international exchange rates," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1986-1989.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1986-1989
    DOI: 10.1016/j.spl.2012.06.030
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    1. McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
    2. Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January.
    3. B. N. Cheng & S. T. Rachev, 1995. "Multivariate Stable Futures Prices," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 133-153, April.
    4. Meerschaert, Mark M. & Scheffler, Hans-Peter, 1999. "Moment Estimator for Random Vectors with Heavy Tails," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 145-159, October.
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    Cited by:

    1. Jensen DR, 2017. "Limits and Inferences for Alpha–Stable Variables," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 4(1), pages 15-18, December.

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