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

Peter Allington peterallington03 at gmail.com
Wed May 22 15:58:32 CEST 2013


Thanks a lot for not giving me up!

I have one last question:
I wondered about, because in my example the Q-Statistics was really
"strong". So the p-values for the lag 3 and 7 were really small
(0.002229 and 0.032980). So this indicates, that there is jointly
autocorrelation, but the plot showes, that there is just one spike
which is slightly significant. Why does this has such a strong impact
on the Q-Statistics? The spike is slightly different (it crosses the
dashed line) and the p-value of the Q-Statistics is already so small?
Why? The other spikes of lag 4 and 5 and so one are not significant?
Why is the p-value of the joint test so small? I would have expect
that there are lots of significant spikes?

Thanks a lot for your wisdom!

2013/5/22 alexios ghalanos <alexios at 4dscape.com>:
> I've traced the difference to the way the residuals method deals with the
> startup values (5 lags) versus the plot which extracts directly the
> standardized residuals used in the likelihood routine.
>
> This gives the same answer:
>
> par(mfrow=c(2,2))
> plot(modelgarch,which=11)
> resdi<-as.numeric(residuals(modelgarch,standardize=TRUE))^2
> Acf(resdi[-c(1:5)])
>
> In most cases this is not likely be significantly different. It is related
> to a problem of how to initialize the ARMA recursion and what to return to
> the user. In THIS case, the first 5 values had an effect which changed the
> visual result marginally. For consistency I guess that the plot should
> return the result one would expect by using the residuals method on the
> model.
>
> Feel free to submit a patch.
>
> Regards,
> Alexios
>
>
> On 22/05/2013 13:40, Jen Bohold wrote:
>>
>> It is not true, that I sent non-reproducible code/examples. I can give you
>> the complete code again and I attach my data. You just have to run the code
>> and you will see, that indeed both plots do differ. So this is replicatable.
>>
>>
>>
>> library(rugarch)
>> myspecification<-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))
>>
>> modelgarch<-ugarchfit(spec=myspecification,data=mydata)
>> plot(modelgarch,which=11)
>>
>>
>> library(forecast)
>> resdi<-as.numeric(residuals(modelgarch,standardize=TRUE))^2
>>
>>
>> Acf(resdi)
>>
>> You can see, that the plots are NOT the same. I do not know, what is wrong
>> with your code and I do not want to offend you, but there is clearly an
>> error in it.
>>
>>
>> ----- Ursprüngliche Message -----
>> Von: alexios ghalanos <alexios at 4dscape.com>
>> An: Jen Bohold <jenbohold at yahoo.de>
>> CC: "r-sig-finance at r-project.org" <r-sig-finance at r-project.org>
>> Gesendet: 13:30 Mittwoch, 22.Mai 2013
>> Betreff: Re: Error in rugarch ACF squared standardized residuals plot
>>
>> I can't replicate your PNG chart differences and here is an example of
>> how you can check:
>> ##########################################
>> library(rugarch)
>> # you specification with YOUR estimated parameters:
>> 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,
>> ar4 = -0.292207, ar5 = -0.745887, ma1=0,ma2=0,ma3=0,
>> ma4 = 0.309446, ma5 = 0.718856, omega = 6e-6, alpha1=0.093397,
>> beta1 = 0.892404))
>> # Simulate a path
>> sim=ugarchpath(modsp, n.sim=5000)
>> # extract the simulated data
>> mydata = as.numeric(fitted(sim))
>> # restate the specification:
>> 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))
>> # estimate the model:
>> modgarch<-ugarchfit(spec=modsp,data=mydata )
>> # extract the standardized residuals:
>> resdi<-as.numeric(residuals(modgarch,standardize=TRUE))
>>
>> # plot:
>> library(forecast)
>> par(mfrow=c(2,2))
>> Acf(resdi^2)
>> plot(modgarch, which=11)
>> ###############################################
>>
>> I don't see ANY differences. You are however welcome to look at the
>> underlying code in the rugarch-plots.R file in the source. If you find a
>> bug you are welcome to submit a patch to the google code repository of
>> the package rather than continuously sending this list PNG attachments
>> and non reproducible code/examples.
>>
>> Regards,
>>
>> Alexios
>>
>>
>> On 22/05/2013 11:49, Jen Bohold wrote:
>>>
>>> Dear Alexios,
>>> thanks a lot for your response!
>>> Yes, this was a typo, so I meant to write
>>>
>>> resdi<-as.numeric(residuals(modgarch,standardize=TRUE))
>>>
>>> and then plot it with
>>>
>>>
>>> Acf(resdi^2)
>>>
>>> this gives a DIFFERENT plot! It is NOT the same!
>>>
>>> Again, I attach both plots.
>>>
>>>
>>>
>>> ----- Ursprüngliche Message -----
>>> Von: alexios ghalanos <alexios at 4dscape.com>
>>> An: Jen Bohold <jenbohold at yahoo.de>
>>> CC: "r-sig-finance at r-project.org" <r-sig-finance at r-project.org>
>>> Gesendet: 11:43 Mittwoch, 22.Mai 2013
>>> Betreff: Re: Error in rugarch ACF squared standardized residuals plot
>>>
>>> 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)
>>>>
>>>
>>
>
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-- 
Peter Allington, M. Sc. CF&RM University of Washington



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