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Convolutions of Heavy Tailed Random Variables and Applications to Portfolio Diversification and MA(1) Time Series


Author Info

  • Jaap Geluk

    (Econometric Institute, Erasmus University Rotterdam)

  • Liang Peng

    (Center for Mathematics and its Applications, Australian National University, Canberra)

  • Casper G. de Vries

    (Erasmus University Rotterdam)


The paper characterizes first and second order tail behavior ofconvolutions of i.i.d. heavy tailed random variables with supporton the real line. The result is applied to the problem of riskdiversification in portfolio analysis and to the estimation of theparameter in a MA(1) model.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 99-088/2.

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Date of creation: 18 Nov 1999
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Handle: RePEc:dgr:uvatin:19990088

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  1. Davis, Richard A. & Dunsmuir, William T.M., 1996. "Maximum Likelihood Estimation for MA(1) Processes with a Root on or near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 12(01), pages 1-29, March.
  2. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
  3. Geluk, J. & de Haan, L. & Resnick, S. & Starica, C., 1997. "Second-order regular variation, convolution and the central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 69(2), pages 139-159, September.
  4. Somnath Datta & William McCormick, 1998. "Inference for the Tail Parameters of a Linear Process with Heavy Tail Innovations," Annals of the Institute of Statistical Mathematics, Springer, vol. 50(2), pages 337-359, June.
  5. Davis, Richard A. & Mikosch, Thomas, 1998. "Gaussian likelihood-based inference for non-invertible MA(1) processes with SS noise," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 99-122, September.
  6. Lii, Keh-Shin & Rosenblatt, Murray, 1992. "An approximate maximum likelihood estimation for non-Gaussian non-minimum phase moving average processes," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 272-299, November.
  7. Jon DANIELSSON & Casper G. DE VRIES, 2000. "Value-at-Risk and Extreme Returns," Annales d'Economie et de Statistique, ENSAE, issue 60, pages 239-270.
  8. de Haan, L. & Pereira, T. Themido, 1999. "Estimating the index of a stable distribution," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 39-55, January.
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