[R-SIG-Finance] Q-Statistics lag order and connection to plot

[Jen Bohold]

Hi,
I am sorry to bother you and the list again, but I have again a problem which I cannot explain to myself:

I fitted a ARMA-GARCH model with the rugarch package of r. The arma is modified, since some parameters are fixed to zero. The relevant output for the explanation of my problem of the model is:


*---------------------------------*
*          GARCH Model Fit*
*---------------------------------*

Conditional Variance Dynamics     
-----------------------------------
GARCH Model    : sGARCH(1,1)
Mean Model    : ARFIMA(5,0,5)
Distribution    : norm 

Optimal Parameters
------------------------------------
        Estimate  Std. Error  t value Pr(>|t|)
ar1     0.000000          NA       NA       NA
ar2     0.000000          NA       NA       NA
ar3     0.000000          NA       NA       NA
ar4    -0.292207    0.019550 -14.9467  0.0e+00
ar5    -0.745887    0.018488 -40.3436  0.0e+00
ma1     0.000000          NA       NA       NA
ma2     0.000000          NA       NA       NA
ma3     0.000000          NA       NA       NA
ma4     0.309446    0.026659  11.6073  0.0e+00
ma5     0.718856    0.021208  33.8952  0.0e+00
omega   0.000006    0.000001   4.2106  2.5e-05
alpha1  0.093397    0.011308   8.2591  0.0e+00
beta1   0.892404    0.012437  71.7563  0.0e+00


Q-Statistics on Standardized Residuals
------------------------------------
                         statistic    p-value
Lag[1]                 7.898       4.949e-03
Lag[p+q+1][11]    21.627     3.312e-06
Lag[p+q+5][15]    27.133     5.374e-05
d.o.f=10
H0 : No serial correlation

Q-Statistics on Standardized Squared Residuals
------------------------------------
                        statistic  p-value
Lag[1]               1.274     0.258961
Lag[p+q+1][3]     9.351    0.002229
Lag[p+q+5][7]    12.135    0.032980
d.o.f=2

My first question belongs to the used lag order in case of the Q-Statistics on Standardized Squared Residuals:
Why is this 3 and 7? As in the case of standardized residuals I would have expect it to be equal to 11 and 15?

Also, if I look at the acf of the standardized squared residuals of the plot method (I attached the plot) you can see, that there is no significant spike. So why is the p-value of lag order 3 and 7 so small? This would mean, that there is serial correlation, which is highly significant, but as the plot shows, all spikes are not significant?

I also attached my data, and my r code is:


library(rugarch)


modsp<-ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(5, 5), include.mean = FALSE), 
distribution.model = "norm",fixed.pars=list(ar1=0,ar2=0,ar3=0,ma1=0,ma2=0,ma3=0))

modgarch<-ugarchfit(spec=modsp,data=mydata)
plot(modgarch)



Thanks a lot for your help,
Jen
-------------- next part --------------
A non-text attachment was scrubbed...
Name: acfstandalvsquared.PNG
Type: image/png
Size: 16874 bytes
Desc: not available
URL: <https://stat.ethz.ch/pipermail/r-sig-finance/attachments/20130520/aca25a5d/attachment.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: mydatagarch.RData
Type: application/octet-stream
Size: 27552 bytes
Desc: not available
URL: <https://stat.ethz.ch/pipermail/r-sig-finance/attachments/20130520/aca25a5d/attachment.obj>