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Fitting a Pareto-Normal-Pareto distribution to the residuals of financial data

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  • Suria Ellis
  • Faans Steyn
  • Hennie Venter

Abstract

The Pareto-Normal-Pareto (PNP) distribution assumes that, for log returns of financial series, the innovations are normally distributed between two threshold values with Pareto tails below and above the respective thresholds. These threshold values can be estimated by maximum likelihood estimation (MLE). Monte Carlo simulations of normal, as well as heavy tailed error distributions, are used to compare the methods using this distribution with other methods to calculate Value-at-Risk (VaR) and Expected Shortfall (ESf). It is also applied to South African stock exchange data. Copyright Physica-Verlag 2003

Suggested Citation

  • Suria Ellis & Faans Steyn & Hennie Venter, 2003. "Fitting a Pareto-Normal-Pareto distribution to the residuals of financial data," Computational Statistics, Springer, vol. 18(3), pages 477-491, September.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:3:p:477-491
    DOI: 10.1007/BF03354611
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    References listed on IDEAS

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    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    3. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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    Cited by:

    1. Grace Lee Ching Yap, 2020. "Optimal Filter Approximations for Latent Long Memory Stochastic Volatility," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 547-568, August.
    2. Glenn, N.L. & Zhao, Yichuan, 2007. "Weighted empirical likelihood estimates and their robustness properties," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5130-5141, June.

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