[R-SIG-Finance] Error in rugarch ACF squared standardized residuals plot
Peter Allington
peterallington03 at gmail.com
Wed May 22 15:59:23 CEST 2013
do not get confused: I answered with my friends account.
2013/5/22 Peter Allington <peterallington03 at gmail.com>:
> 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
--
Peter Allington, M. Sc. CF&RM University of Washington
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