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 -------------- next part -------------- An embedded and charset-unspecified text was scrubbed... Name: Garch.csv URL: <https://stat.ethz.ch/pipermail/r-sig-finance/attachments/20090216/b67503c4/attachment.pl>
odd GARCH(1,1) results
4 messages · Helena Richter, Adams, Zeno, Eric Zivot +1 more
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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 _______________________________________________ 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.
1 day later
If your data is correct, I see very high auto-correlation in first few lags. Which is natural in returns for higher frequencies. Therefore a mere gacch(1,1) specification may not be correct here. Have you tried with arma-garch specification?
Helena Richter wrote:
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 0.0101469753486814 0.0302708525301284 0.0298869542573102 0.0250238066360943 0.0219854269480636 0.0255910978745133 0.0208766939739549 0.024472384972313 0.0104622603956565 0.0156958456499357 0.00856720663997033 0.00554233092097657 0.0178169931968505 0.0210859439733833 0.0237885580502165 0.0167733305146503 0.0188592789433067 0.0135089788757992 0.0240819536500512 0.0184436895969784 0.0353754332617942 0.0321898629583924 0.0217899667893017 0.0172398497190095 0.0163914150178588 0.0201309274983712 0.0338013250091364 0.0361931688792124 0.0325828765178621 0.0287244326640976 0.0253523402633412 0.0175501402847404 0.0252357634588918 0.0374920819481566 0.0326047940338621 0.0534817989667282 0.0426675454652661 0.0223149096583253 0.0274987474190061 0.0246657927597472 0.0319013714312724 0.0297229546082391 0.0222133631437097 -0.00499102835204226 -0.0100445943888354 -0.0305945586081492 -0.0295261769725028 -0.0163888329648776 -0.0322053226938304 -0.0243851116782977 -0.0344066186625488 -0.0309734197068084 -0.0450769173663317 -0.037850073973392 -0.0205237352329365 -0.0136852813721192 -0.0142612563819063 -0.0133534576292516 0.0133184076877491 0.00491571150380778 0.0253169375424642 0.0341114006741854 0.0390611810003106 0.0346856037825977 0.0311649689770797 0.011488947602242 0.0232081050895178 0.0276265045794663 0.0129717174745311 0.00163794296612078 -0.024949441008574 -0.0292122997648142 -0.0228978631488851 -0.00109151628878845 0.00330215163389701 0.0302721218697545 0.0129328948578658 0.0167299192156694 0.0227293766139797 0.0362692295589419 0.0453879999373127 0.0277697471036363 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