[R-SIG-Finance] Error in rugarch ACF squared standardized residuals plot

[alexios ghalanos]

Dear Jen,

The reason I have not answered is that you post one question, then 
instead of patiently waiting for an answer, you very shortly post more 
and more followups. As I said in a previous email, the likelihood of 
answering, at least on my part, will depend on the effort shown to at 
least try to do your own research and the framing of the question. You 
also seem to be cross-posting to stackexchange.

With regards to your specific question, you are wrong and this is seen 
by your own code:

resdi<-as.numeric(residuals(mydata,standardize=TRUE))

This is NOT the standardized residuals of the model but the 
observations, so that when you compare to the Acf plot you are comparing 
the observations (before the estimation) to the standardized residuals 
(after the ARMA filtration).

You probably wanted to write:

resdi<-as.numeric(residuals(modgarch,standardize=TRUE))

The plots of the results from rugarch are the same with what you get 
with the Forecast package (which is actually a wrapper for the stats 
package 'plot.acf').

I'm going to politely ask you to please take some more care when posting 
and making such grand statement as "plot are not useable anymore". You 
are quickly burning through any remaining goodwill left on the part of 
this developer. Finally, I would suggest an excellent reference such as 
Zivot and Wang ("Modeling Financial Time Series with S-PLUS") or Tsay 
("Analysis of Financial Time Series") which may help you answer some of 
your many questions.

Regards,

Alexios



On 22/05/2013 08:10, Jen Bohold wrote:
> Although it seems that there is no feedback and you do not want to comment on me, I thought I should share this to the list, maybe someone else is some time wondering about this (maybe I did a mistake, but no one of the list or you told me in the previous mail). Also, I do not want to offend you, I like your package it's great! Especially I liked the acf plots, they have a better design, although
> you will see in the following text, that the "ACF of Squared Standadrized Residuals" plot are not useable anymore.
>
>
> The plot of the ACF of the squared standardized residuals in rugarch output (you get it via plot(yourmodel) and choosing number 11) is wrong.
> However, the corresponding Q-Statistics of the rugarch output are correct!
>
> Consider the following (I attached my data and the plots). I fitted the following model (output extracted to the relevant parts):
>
> *---------------------------------*
> *          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
> As you can see in the "Q-Statistics on Standardized Squared Residuals" there is clearly correlation in the standardized squared residuals. BUT if you look at the plot with the plot method and choosing number 11 you can see, that NO spike is significant.
>
> This plot is not correct, I controlled it via the Acf plot of the forecast package and clearly, the spikes are larger! So the second spike is now significant. I control the calculations via the Box.test method using d.o.f.=2 and choosing the lag 3 and 7 and the calculations in the rugarch package are correct! So the p-values are indeed 0.002229 and 0.032980. So why is the plot of the rugarch package wrong?
>
> One further notice: In a previous mail, I asked, why the lags in the Q-Statistics on Standardized Squared Residuals are different to the lags used in Q-Statistics on Standardized Residuals. Of course, I have now seen, that the second uses the GARCH parameters, so it is clear, that this has to be equal to two (1+1). I also have to say, that I think, that the ACF of observations plot e.g. is indeed correct (number 4), so it seems, that the plot number 11 uses different scaled residuals? Maybe it uses the non-standardized squared residuals? Could that be the reason?
>
> Thanks a lot for your notice.
> My code:
>
> 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)
>
>
> residuals(mydata,standardize=TRUE)
> resdi<-as.numeric(residuals(mydata,standardize=TRUE))
>
> library(forecast)
> Acf(resdi^2)
>
> Box.test(resdi^2, lag = 3, type = "Ljung-Box", fitdf = 2)
> Box.test(resdi^2, lag = 7, type = "Ljung-Box", fitdf = 2)
>