[R-sig-finance] Convergence problems in garch(1,1)

[Ajay Shah]

On Thu, Aug 26, 2004 at 09:06:02AM +0200, Gregor.gawron at rmf.ch wrote:
> I don't get this messege. Maybe, a different sample lenght will help. In
> fact, in my original code I am using a different data than the DAX. I
> took DAX just for illustrative purposes since the data is available in
> 'tseries' package.

Hmm, if I do:

     library(tseries)
     data(EuStockMarkets)  
     dax <- diff(log(EuStockMarkets))[,"DAX"]
     m1 <- garch(dax)  # Fit a GARCH(1,1) to DAX returns

all is well. But if I say:

     m2 <- garch(dax[1:1500])

I get:

 ***** ESTIMATION WITH ANALYTICAL GRADIENT ***** 


     I     INITIAL X(I)        D(I)

     1     0.738721E-04     0.100E+01
     2     0.500000E-01     0.100E+01
     3     0.500000E-01     0.100E+01

    IT   NF       F        RELDF    PRELDF    RELDX   STPPAR   D*STEP   NPRELDF

     0    1 -0.631E+04
     1    9 -0.631E+04  0.12E-06  0.25E-06  0.1E-05  0.1E+12  0.1E-06  0.16E+05
     2   20 -0.631E+04  0.39E-03  0.89E-03  0.4E+00  0.2E+01  0.1E+00  0.26E+00
     3   22 -0.631E+04  0.73E-03  0.13E-02  0.5E+00  0.2E+01  0.2E+00  0.17E+00
     4   24 -0.631E+04  0.14E-03  0.19E-03  0.8E-01  0.1E+01  0.6E-01  0.34E-03
     5   27 -0.632E+04  0.94E-03  0.66E-03  0.2E+00  0.3E+00  0.2E+00  0.18E-02
     6   39 -0.632E+04  0.75E-04  0.12E-03  0.8E-06  0.4E+01  0.1E-05  0.86E-01
     7   40 -0.632E+04  0.24E-06  0.32E-06  0.8E-06  0.2E+01  0.1E-05  0.93E-01
     8   50 -0.632E+04  0.39E-03  0.36E-03  0.5E-01  0.2E+01  0.6E-01  0.92E-01
     9   52 -0.633E+04  0.69E-03  0.88E-03  0.8E-01  0.2E+01  0.1E+00  0.14E+01
    10   60 -0.633E+04  0.39E-04  0.86E-04  0.2E-06  0.6E+01  0.4E-06  0.35E-03
    11   61 -0.633E+04  0.11E-05  0.12E-05  0.2E-06  0.2E+01  0.4E-06  0.14E-03
    12   70 -0.633E+04  0.94E-11  0.52E-09  0.1E-09  0.1E+02  0.2E-09  0.14E-03
    13   83 -0.633E+04 -0.20E-14  0.43E-13  0.1E-13  0.1E+06  0.2E-13  0.14E-03

 ***** FALSE CONVERGENCE *****

 FUNCTION    -0.632703E+04   RELDX        0.122E-13
 FUNC. EVALS      83         GRAD. EVALS      13
 PRELDF       0.431E-13      NPRELDF      0.137E-03

     I      FINAL X(I)        D(I)          G(I)

     1    0.840058E-05     0.100E+01     0.135E+05
     2    0.699397E-01     0.100E+01     0.721E+02
     3    0.832688E+00     0.100E+01     0.371E+01




The two estimates differ considerably, so it _does_ seem to be a case
of "false convergence":

> m1

Call:
garch(x = dax)

Coefficient(s):
       a0         a1         b1  
4.639e-06  6.833e-02  8.891e-01  

> m2

Call:
garch(x = dax[1:1500])

Coefficient(s):
       a0         a1         b1  
0.0000084  0.0699397  0.8326876  

-- 
Ajay Shah                                                   Consultant
ajayshah at mayin.org                      Department of Economic Affairs
http://www.mayin.org/ajayshah           Ministry of Finance, New Delhi