Re: [Gretl-users] Convergence is not met
On Wed, 11 Jan 2006, Seung Hun Han wrote:
when i estimate the garch parameter of cj stock price during 1 year
data
using gretl and R.
IN Gnu-R.
> garch(x,c(1,1))
... [snip] ...
Note here:
***** FALSE CONVERGENCE *****
FUNCTION -0.849489E+03 RELDX 0.114E-13
FUNC. EVALS 78 GRAD. EVALS 21
PRELDF 0.477E-13 NPRELDF 0.231E-06
I FINAL X(I) D(I) G(I)
1 0.167570E-05 0.100E+01 0.188E+04
2 0.630399E-01 0.100E+01 0.113E+01
3 0.944707E+00 0.100E+01 0.364E+00
and here
Warning message:
NANs... in: sqrt(pred$e)
Note that the sum of the 2 garch parameters alpha and beta exceeds 1. In
these cases, the GARCH model is simply not appropriate (it must be said
that your sample is a bit small for garch estimation).
On the same data, Eviews gives:
C 0.001085 0.001262 0.860183 0.3897
C 3.01E-06 3.16E-06 0.953145 0.3405
ARCH(1) 0.056867 0.018513 3.071698 0.0021
GARCH(1) 0.946872 0.019763 47.91246 0.0000
and you have the same problem.
Laurent's ox package gives
Maximum Likelihood Estimation (Std.Errors based on Second derivatives)
Coefficient Std.Error t-value t-prob
Cst(M) 0.001329 0.0011434 1.163 0.2461
Cst(V) 0.016847 0.053572 0.3145 0.7534
ARCH(Alpha1) 0.062022 0.020664 3.001 0.0030
GARCH(Beta1) 0.945226 0.025128 37.62 0.0000
and you have the same problem again.
In circumstances such as these, gretl concludes there is no convergence.
Actually, after 3 iterations the gretl algorithm lands onto
Parameters and gradients at iter. 3
0.078722 (-4.495820)
0.006162 (150.511348)
0.059888 (103.997100)
0.940112 (122.291993)
and refuses to go further because following the optimisation algorithm
you'd go outside the admissible parameter space.
See also the thread on this same list about a month ago:
http://ricardo.ecn.wfu.edu/pipermail/gretl-users/2005-December/
Hope this helps,
Riccardo `Jack' Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
jack(a)dea.unian.it
http://www.econ.univpm.it/lucchetti