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

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • Jaap Geluk & Liang Peng & Casper G. de Vries, 1999. "Convolutions of Heavy Tailed Random Variables and Applications to Portfolio Diversification and MA(1) Time Series," Tinbergen Institute Discussion Papers 99-088/2, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:19990088
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    References listed on IDEAS

    as
    1. Geluk, J.L. & Peng, L., 1999. "An adaptive optimal estimate of the tail index for MA(1) time series," Econometric Institute Research Papers EI 9910-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. 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(1), pages 1-29, March.
    3. 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.
    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;The Institute of Statistical Mathematics, vol. 50(2), pages 337-359, June.
    5. William L. Miller, 1972. "Herbert Spencer's Theory of Welfare and Public Policy," History of Political Economy, Duke University Press, vol. 4(1), pages 207-231, Spring.
    6. Jon Danielsson & Casper G. De Vries, 2000. "Value-at-Risk and Extreme Returns," Annals of Economics and Statistics, GENES, issue 60, pages 239-270.
    7. 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.
    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.
    9. 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.
    10. 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.
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