*
* Example 7.6 from pp 313-314
*
open data d-ibmln98.dat
data(format=free,org=columns) 1 9190 ibmlog
*
nonlin k alpha beta
*
* Get series of minima over 63 period windows. MVSTATS will compute these over
* moving overlapping windows. The SAMPLE instruction is used to pull out every
* 63rd element. It defines %NOBS as the number of data points extracted.
*
compute n=63
mvstats(min=mins,max=maxs,span=n) ibmlog
sample(smpl=%clock(t,n)==n) mins / r 1
compute gend = %nobs
compute alpha=.8,beta=-2.0,k=-.2
*
* Because the GEV distribution is designed for modelling maximum values, we flip
* signs on both r and beta to transform the minimum problem to a maximum problem.
*
frml gevmin = %loggevdensity(-r,k,-beta,alpha)
maximize gevmin 1 gend
*
* Similarly, the beta needs to be sign-flipped in inverting the GEV distribution
* to get a left tail.
*
compute var01=%invgev((1-.01)**n,k,-beta,alpha)
compute var05=%invgev((1-.05)**n,k,-beta,alpha)
disp "1% VaR with n=63" -var01
disp "5% VaR with n=63" -var05
*
* Repeat with n=21
*
compute n=21
mvstats(min=mins,max=maxs,span=n) ibmlog
sample(smpl=%clock(t,n)==n) mins / r 1
compute gend = %nobs
maximize gevmin 1 gend
*
compute var01=%invgev((1-.01)**n,k,-beta,alpha)
compute var05=%invgev((1-.05)**n,k,-beta,alpha)
disp "1% VaR with n=21" -var01
disp "5% VaR with n=21" -var05