fGarch: sqp algorithm

[Yohan Chalabi]

Michal,

the default optimization is now nlminb. The paper you mentioned has
been written a while ago with an older version of fGarch. The
documentation page has been updated since.

The optimization of ARMA-APARCH mdodels can be problematic due to its
non-convex nature and the optimization can be very sensitive to the
initial values. Different initial values might lead to different
results!

This is one of the reason we offer different optimization routines in
garchFit, so the user can choose which routine fits best his needs. 
You can also change most of the optimization options through the
control list argument. 

Note we introduced a new optimization routine in the development branch
of fGarch : "mnfb". See the documentation page for more information. So
far, it gives very good results. Let me know if it works for you!

An other common problem in optimization is a badly scaled problem. This
can lead to weird results due to machine errors in the optimization.
This is the reason we multiply the sp500dge series by 100 before we
optimize it!


# with fGarch rev. 2641
library(fGarch)
data(sp500dge)
x <- 100*sp500dge[,1]
garchFit(~arma(0,1)+aparch(1,1), x, algorithm="mnfb")
# or
garchFit(~arma(0,1)+aparch(1,1), x)


give the same results as in the mentionned paper.

regards,
Yohan