Extreme Events – Specimen Question A.2.3

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You discover that the periods being used for Index A are quite long (e.g. yearly), sufficiently long for secular change to make the relevance of data from some of the earlier periods suspect. You decide to exponentially weight the data using a half-life of 10 periods, i.e. the weight given to period   (for ) is .


(a)    Recalculate the mean, standard deviation, skew and kurtosis weighting the data as above. Are they still suggestive of fat-tailed behaviour?




(b)   Prepare a quantile-quantile plot of the weighted data. Is it also suggestive of fat-tailed behaviour? Hint: the ‘expected’ values for such plots need to bear in mind the weight given to the observation in question.




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