
I checked your data using different model specifications and options in EViews. It seems that the parameters have been estimated correctly (different error distributions, optimization algorithms or asymmetric parameters do not change the estimated parameter values by much). I think the line graph supports the model parameters: the data is mainly driven by shocks (high alpha) but the shocks are not very persistent (low beta). I know that the DAX series normally produces parameter estimates of around 0.05 for alpha and 0.9 for beta using daily data but you may have just picked an awkward period (although 2300 is pretty long). 

-----Original Message-----
From: r-sig-finance-bounces@stat.math.ethz.ch on behalf of Helena Richter
Sent: Mon 2/16/2009 5:55 PM
To: r-sig-finance@stat.math.ethz.ch
Subject: [R-SIG-Finance] odd GARCH(1,1) results
 
Hi everybody,

I'm trying to fit a Garch(1,1) process to the DAX returns. My data 
consists of about 2300 10day-logreturns in chronologically descending 
order (see attachment). But if I use the garch function I get a very 
high alpha_1 and a quite low beta, which doesn't make that much sense. I 
think I am missing something, but have no idea what it might be. I'd 
appreciate it a lot if someone could have a look at the output I posted 
at the end of this mail. Maybe there's something an experienced user 
might see at once. I also tried the garchFit function with nearly the 
same results.
I'm very thankful for every answer. Please excuse my bad english.
Helena


 > g2005out<-garch(g2005,order=c(1,1))

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


I INITIAL X(I) D(I)

1 2.214508e-03 1.000e+00
2 5.000000e-02 1.000e+00
3 5.000000e-02 1.000e+00

IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF
0 1 -5.974e+03
1 6 -5.998e+03 3.91e-03 5.51e-03 3.6e-03 2.5e+08 3.6e-04 6.90e+05
2 7 -6.000e+03 3.19e-04 6.17e-04 3.1e-03 2.0e+00 3.6e-04 5.50e+02
3 8 -6.001e+03 2.76e-04 2.98e-04 3.5e-03 2.0e+00 3.6e-04 5.21e+02
4 13 -6.161e+03 2.59e-02 3.79e-02 4.8e-01 2.0e+00 9.3e-02 5.07e+02
5 21 -6.182e+03 3.39e-03 7.77e-03 1.1e-03 3.6e+00 3.2e-04 4.87e-01
6 22 -6.182e+03 9.68e-05 7.28e-05 1.1e-03 2.0e+00 3.2e-04 2.11e+00
7 23 -6.183e+03 2.15e-05 2.25e-05 1.1e-03 2.0e+00 3.2e-04 2.37e+00
8 29 -6.213e+03 4.86e-03 4.50e-03 5.7e-01 2.0e+00 1.6e-01 2.34e+00
9 31 -6.278e+03 1.03e-02 1.04e-02 4.3e-01 2.0e+00 3.2e-01 1.65e+02
10 33 -6.301e+03 3.67e-03 5.01e-03 2.9e-02 1.9e+00 3.2e-02 7.66e-02
11 36 -6.347e+03 7.26e-03 7.63e-03 1.0e-01 1.3e+00 1.3e-01 1.06e-01
12 37 -6.399e+03 8.17e-03 9.09e-03 2.1e-01 7.0e-01 2.6e-01 1.33e-02
13 39 -6.412e+03 2.04e-03 2.19e-03 2.6e-02 1.8e+00 2.6e-02 2.18e-02
14 41 -6.437e+03 3.80e-03 5.84e-03 9.4e-02 1.1e+00 1.0e-01 1.80e-02
15 43 -6.498e+03 9.44e-03 8.74e-03 2.9e-01 8.5e-02 3.2e-01 8.77e-03
16 44 -6.518e+03 3.07e-03 2.11e-03 9.0e-02 0.0e+00 8.9e-02 2.11e-03
17 45 -6.527e+03 1.38e-03 1.07e-03 7.2e-02 0.0e+00 8.3e-02 1.07e-03
18 46 -6.530e+03 4.03e-04 3.24e-04 4.9e-02 0.0e+00 7.6e-02 3.24e-04
19 47 -6.530e+03 6.83e-05 7.29e-05 1.7e-02 0.0e+00 2.4e-02 7.29e-05
20 48 -6.530e+03 5.26e-06 6.29e-06 6.2e-03 0.0e+00 1.2e-02 6.29e-06
21 49 -6.530e+03 1.53e-07 1.54e-07 9.0e-04 0.0e+00 1.7e-03 1.54e-07
22 50 -6.530e+03 1.33e-10 1.22e-10 2.3e-05 0.0e+00 3.3e-05 1.22e-10
23 51 -6.530e+03 2.08e-12 6.94e-12 3.9e-06 0.0e+00 6.0e-06 6.94e-12

***** RELATIVE FUNCTION CONVERGENCE *****

FUNCTION -6.530104e+03 RELDX 3.860e-06
FUNC. EVALS 51 GRAD. EVALS 24
PRELDF 6.944e-12 NPRELDF 6.944e-12

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

1 2.041120e-04 1.000e+00 4.584e-01
2 7.096202e-01 1.000e+00 2.579e-04
3 2.487274e-01 1.000e+00 3.097e-04

 > summary(g2005out)

Call:
garch(x = g2005, order = c(1, 1))

Model:
GARCH(1,1)

Residuals:
Min 1Q Median 3Q Max
-4.1857 -0.6978 0.3268 0.9039 4.9820

Coefficient(s):
Estimate Std. Error t value Pr(>|t|)
a0 2.041e-04 2.072e-05 9.849 <2e-16 ***
a1 7.096e-01 5.780e-02 12.277 <2e-16 ***
b1 2.487e-01 2.062e-02 12.060 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Diagnostic Tests:
Jarque Bera Test

data: Residuals
X-squared = 33.1741, df = 2, p-value = 6.257e-08


Box-Ljung test

data: Squared.Residuals
X-squared = 8.9147, df = 1, p-value = 0.002829








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