Question on Extreme Value Calibration - Generalised Pareto Distribution

[James Sharpe]

Hello,

I am working as part of the Extreme Events Working Party with
the UK Institute of Actuaries.  We
have looked at the QRMlib package and the fExtremes package for use in R to
calibrate the Generalised Pareto Distribution.  Using the attached data we found
nearly identical results for calibrating the GPD using the maximum likelihood
estimate; but quite different results for the probability weighted moments
estimate.

Could I ask if you are aware of this issue – or found
something similar?  The code
used is below:

setwd("C:/EVT")

a<-read.csv("returns.csv",header=T)

attach(a)

library(QRMlib)

library(fExtremes)

k<-c(UK,AUD,BEL,CAN,DEN,FRA,GER,IRE,ITA,JAP,NET,SAF,SPA,SWE,SWZ,US)

Data<--GER

fGPD<-gpdFit(Data,0.1)

GPD<-fit.GPD(Data,0.1)

fGPDpwm<-gpdFit(Data,0.05,type =
"pwm")

GPDpwm<-fit.GPD(Data,0.05,method="pwm")

GPD$par.ests

GPDpwm$par.ests

fGPD

fGPDpwm

 

I tried with various data strings and
thresholds in the table below highlighting the difference in the PWM
calibration method:


 
  
  Threshold
  -1% 
  
  
  99.5th
  
  
  Xi
  
  
  B
  
 
 
  
  UK
  
  
  MLE
  QRMlib
  
  
  42.2%
  
  
  0.0338
  
  
  0.0979
  
 
 
  
   
  
  
  PWM
  QRMlib
  
  
  47.9%
  
  
  0.1643
  
  
  0.0847
  
 
 
  
   
  
  
  MLE
  fExtreme
  
  
  42.3%
  
  
  0.0339
  
  
  0.0979
  
 
 
  
   
  
  
  PWM
  fExtreme
  
  
  44.0%
  
  
  0.0760
  
  
  0.0936
  
 
 
  
  France
  
  
  MLE
  QRMlib
  
  
  37.2%
  
  
  -0.2432
  
  
  0.1401
  
 
 
  
   
  
  
  PWM
  QRMlib
  
  
  43.1%
  
  
  -0.0809
  
  
  0.1213
  
 
 
  
   
  
  
  MLE
  fExtreme
  
  
  37.2%
  
  
  -0.2430
  
  
  0.1401
  
 
 
  
   
  
  
  PWM
  fExtreme
  
  
  39.2%
  
  
  -0.1801
  
  
  0.1325
  
 
 
  
  Germany
  
  
  MLE
  QRMlib
  
  
  69.5%
  
  
  -0.0134
  
  
  0.1729
  
 
 
  
   
  
  
  PWM
  QRMlib
  
  
  72.3%
  
  
  0.0248
  
  
  0.1664
  
 
 
  
   
  
  
  MLE
  fExtreme
  
  
  69.5%
  
  
  -0.0134
  
  
  0.1729
  
 
 
  
   
  
  
  PWM
  fExtreme
  
  
  66.0%
  
  
  -0.0644
  
  
  0.1816
  
 
 
  
  Italy
  
  
  MLE
  QRMlib
  
  
  45.9%
  
  
  -0.3418
  
  
  0.2030
  
 
 
  
   
  
  
  PWM
  QRMlib
  
  
  48.2%
  
  
  -0.2821
  
  
  0.1934
  
 
 
  
   
  
  
  MLE
  fExtreme
  
  
  45.9%
  
  
  -0.3418
  
  
  0.2030
  
 
 
  
   
  
  
  PWM
  fExtreme
  
  
  43.9%
  
  
  -0.3946
  
  
  0.2104
  
 
 
  
  Spain
  
  
  MLE
  QRMlib
  
  
  35.4%
  
  
  -0.2968
  
  
  0.1463
  
 
 
  
   
  
  
  PWM
  QRMlib
  
  
  41.5%
  
  
  -0.1071
  
  
  0.1236
  
 
 
  
   
  
  
  MLE
  fExtreme
  
  
  35.4%
  
  
  -0.2963
  
  
  0.1462
  
 
 
  
   
  
  
  PWM
  fExtreme
  
  
  37.7%
  
  
  -0.2124
  
  
  0.1353
  
 


 

 

I would be interested to know if you have any ideas where
the approach may differ eg different sub algorithms used, different calculation
order etc... Any pointers would be very much appreciated.


Many thanks



Best regards

James Sharpe 		 	   		  
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