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

Mon Feb 16 22:50:39 CET 2009

Everything doesn't have to be a GARCH(1,1) model. Look at the
autocorrelations of the squared returns. It could be that a pure ARCH
process is most appropriate for this series. The GARCH(1,1) model gives
reasonably slow mean reversion.  

-----Original Message-----
From: r-sig-finance-bounces at stat.math.ethz.ch
[mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Adams, Zeno
Sent: Monday, February 16, 2009 1:20 PM
To: Helena Richter; r-sig-finance at stat.math.ethz.ch
Subject: Re: [R-SIG-Finance] odd GARCH(1,1) results

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 at stat.math.ethz.ch on behalf of Helena Richter
Sent: Mon 2/16/2009 5:55 PM
To: r-sig-finance at 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

EBS European Business School gemeinnuetzige GmbH - Sitz der Gesellschaft:
Wiesbaden, Amtsgericht Wiesbaden HRB 19951 - Umsatzsteuer-ID DE 113891213
Geschaeftsfuehrer: Prof. Dr. Christopher Jahns,  Rektor/CEO; Dr. Reimar
Palte,  Kanzler/CFO;  Sabine Fuchs, CMO; Verwaltungsrat: Dr. Hellmut K.
Albrecht, Vorsitzender
	[[alternative HTML version deleted]]

_______________________________________________
R-SIG-Finance at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only.
-- If you want to post, subscribe first.