[R-SIG-Finance] odd GARCH(1,1) results

[Helena Richter]

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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