[R-SIG-Finance] Conflicting "spd" function estimates

Gareth McEwan mcewan.gareth at gmail.com
Wed Oct 29 18:30:51 CET 2014


Hi there

I have searched high and low, but haven't found how to combine a parametric
GPD fitting of upper and lower tails to a non-parametric Gaussian kernel
interior. So I need to go with the "spd" function, but I have quite
conflicting results using this function.

spd.fit.ALBI=spdfit(sorted.ALBI.std.resids, upper=0.9, lower=0.1,
tailfit="GPD", type="mle", kernelfit="normal", information="observed")
show(spd.fit.ALBI)
Output:
# Upper Tail: Threshold = 1.22226
The above tail threshold is different to 1.218522 using the quantile
function on the same data at the same 90% cutoff point.
# Estimated Parameters
#     xi           beta
#   -0.18608   0.48698
These estimates are different to -0.1996078 and 0.4973661, respectively
(using "evir", "ismev" and "fExtremes" packages), but far more so than the
estimates below..

# Lower Tail: Threshold = -1.22126 (compared to -1.213646 using quantile
function on negative of the sorted.ALBI.std.resids, at the equivalent of a
10% cutoff point)
# Estimated Parameters
#     xi           beta
#    0.06574   0.76526
These estimates are quite different to the 0.1051834 and  0.7098641,
respectively, using the abovementioned packages.

I am aware that there are only a few data points used in the fitting, so
would this sort of discrepancy be acceptable?

I am not sure how the "spdfit" function selects the upper and lower tail
thresholds (versus the quantile function I am using from literature), but I
think the manner in which the thresholds are selected is what contributes
to the conflicting estimates. Is there a way I can improve my technique at
all? I would prefer to combine the upper tail, interior and lower tail
manually, but I would need help putting it together. The next best option
is the "spd" function, but I'd like to know if the evident discrepancies
would be acceptable?

Many thanks
Gareth

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