Extreme Events – Specimen Question A.2.3
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Question and Answer Summary
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?
Answer/Hints
(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.
Answer/Hints
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