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Fig. 1. 1000 day excerpt from series of negative log returns on Standard and Poors index containingcrash of 1987; lower plot shows estimate of the conditional standard deviation derived from PMLfitting of AR 1 –GARCH 1,1 model.Ž .Ž.
Fig. 2. Correlograms for the raw data and their absolute values as well as for the residuals and absoluteresiduals
Fig. 3. Quantile–quantile plot of residuals against the normal distribution shows residuals to beleptokurtotic.
Table 1Threshold values and maximum likelihood GPD parameter estimates used in the construction of tail
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