Extreme Events – Specimen Question
A.2.1(c) – Answer/Hints
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Q. Prepare a standardised
quantile-quantile plot for Index A. Does it appear to be fat-tailed?
A standardised quantile-quantile plot for Index A can be
derived using the following steps:
i.
Standardise the data, i.e. if the original logged returns are then
calculate:
where is the
sample mean and is the sample
standard deviation
ii.
Order this data, i.e. calculate where is the
smallest value of the set , is the
next smallest etc.
iii.
Calculate the ‘expected’ value that we would expect each of the to take
were they to be coming from a normal distribution, i.e.
iv.
Plot the against
the , usually
with the along the
horizontal axis and the along the
vertical axis.
Steps (i) to (iii) can be all be carried out without too
much effort on a case-by-case basis in a spreadsheet system such as Microsoft
Excel or using the Nematrian web functions MnNormaliseArray (to
carry out steps (i) and (ii) and MnStandardisedNormalQuantilesArray
(to carry out step (iii)).
However, it is simpler to use the Nematrian website charting
capability. This includes a web function, i.e. MnPlotStandardisedQQ,
which both creates (internally) the required data to be viewed in a
standardised QQ-plot (i.e. carries out steps (i) to (iii) above) and also
creates a temporary Nematrian ‘SmartChart’, i.e. the plot itself as in step
(iv), accessible via a suitable ‘SmartCode’. As with other Nematrian web
functions it is possible to access the function programmatically (in which case
it merely returns the temporary ‘SmartCode’ assigned to the relevant
‘SmartChart’). It can also be accessed interactively, in which case the output
on the webpage includes both the ‘SmartCode’ and the SmartChart.
For users with appropriate permissions, temporary
SmartCharts can be converted into permanent SmartCharts, which are stored
permanently on the Nematrian website and retain an association between the
creator of the chart, its underlying data and its visual form. These can be
copied and pasted from the Nematrian website into other venues, e.g. Word
documents or Powerpoint presentations. For users without these permissions the
image forming the SmartChart can be copied in a manner similar to any other
image you might find on a webpage, but what is copied no longer retains an
association with its creator and its underlying data.
A permanent SmartChart answering this question is:
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