[R-SIG-Finance] rugarch VaR calculation "manually"

[Neuman Co]

Thanks a lot for your help, ok, I added the signature in my mail and
the r sig list accout.

But to be honest neither I am not really understanding you nor are
your hints helping me. From someone other, I was told to use the
following code to get what I want:

(I add my model here specification again, so you do not have to search
in my posts before)

-----------------------------------------------------------------------------------
library(rugarch)
alvdatemod<-alvdate[-1]
alvgarchdata<-data.frame(alvlloss,row.names=alvdatemod)

alvnomodel<-ugarchspec(variance.model = list(model = "sGARCH",
garchOrder = c(1, 1)),
mean.model = list(armaOrder = c(0, 0), include.mean = FALSE),
distribution.model = "norm")

alvnomodelgarch<-ugarchfit(spec=alvnomodel,data=alvgarchdata)
#plot(alvnomodelgarch)
-------------------------------------------------------------------------------------


and here comes the relevant part:


spec = getspec(alvnomodelgarch);
setfixed(spec) <- as.list(coef(alvnomodelgarch));
forecast = ugarchforecast(spec, n.ahead = 1, n.roll = 2579, data =
alvgarchdata[1:2580, ,drop=FALSE], out.sample = 2579);
sigma(forecast);
fitted(forecast)


I get the (german) error message after the sigma command:
Fehler in UseMethod("sigma") :
  nicht anwendbare Methode für 'sigma' auf Objekt der Klasse
"c('uGARCHforecast', 'GARCHforecast', 'rGARCH')" angewendet

And the forecast specification is also not what I want, if you just
look at forecast, you will see, that again I just got one value, this
is NOT what I want!

Also, I am not understanding why I have to use this n.roll number and
this out.sample number. Also, why can't I just use my dataset, but
instead use [1:2580, ,drop=FALSE] ? But these are just some smaller
unimportant questions.



Later on, I want to calculate the VaR and compare it to the quantile
method, therefore I would continue with the following idea, first,
calculate VaR:

VaR=fitted(forecast)+sigma(forecast)*qnorm(0.99)

and then compare it to the quantile method:

quantile(forecast,probs=0.99)

but it seemed, that I also did a syntax error here.


2013/5/8 alexios ghalanos <alexios at 4dscape.com>:
> That may be the case for your linear regression example, but certainly NOT
> the case in the ARMA-GARCH models. Everything is based on information upto
> time T-1. There is no "contemporaneous" data, as a reading of the vignette
> (where the models are clearly explained and formulated) shows. Therefore,
> and as pointed out before, USE the fitted, sigma, and quantile methods.
>
> -Alexios
>
>
> On 08/05/2013 12:06, Neuman Co wrote:
>>
>> well but this is exactly the point, that
>>
>> ugarchforecast(alvnomodelgarch, n.ahead = 1)
>>
>> just gives me one forecast, but I want to have this from my beginning
>> of the time series up to the end. So I do not want to exclude these
>> observations in my fitting. I want to use all observations for my
>> fitting and then do one step ahead in sample predictions. So e.g. I
>> have a time series of 1000 observations. I to the fitting with the
>> 1000 observations and then I want to predict the one step ahead
>> in-sample forecasts of the cond. mean and the cond. volatility?
>>
>> I do not understand the thing with the fitted and the sigma. Correct
>> me if I am wrong, but these are the fitted values, these are not
>> 1-step-ahead forecasts?
>>
>> I try to give a more simpler example to make the understanding easier:
>> consider a simple linear regression:
>> The fitted values of y at time point t use the realization of x at
>> time point t. The one step ahead forecast uses the realization of
>> timepoint minus 1.
>>
>> So I do NOT want to have the fitted values of the cond. volatility and
>> the cond. mean (in my case the cond. mean is zero, because I have
>> specified no model for it), but the one step ahead forecasts of it. So
>> R should do the n.ahead=1 not only for the last value, but from the
>> beginning up to the end?
>>
>> I mean I only get the forecast of the next day, the 2013-03-04, but I
>> want to have it from the beginning up to the end?
>>
>>
>>
>>
>>
>>
>> 2013/5/8 alexios ghalanos <alexios at 4dscape.com>:
>>>
>>> Please TRY to send one question, wait for a reply and then ask another
>>> rather than sending 3 emails in a row.
>>>
>>> 1. The only reason that you would not get an xts returned object in the
>>> example below is that you are using an old version of rugarch. Make sure
>>> you
>>> download the latest version (which requires R>=3.0.0) and update your
>>> packages. It is also good practice to send the output of
>>> sessionInfo() in such cases.
>>>
>>> 2. I'm not sure what you mean by "one step ahead in sample predictions".
>>> - If you want the 1-ahead forecast use ugarchforecast(alvnomodelgarch,
>>> n.ahead = 1)
>>> - If you want the in-sample estimated values use 'fitted' and 'sigma'
>>> (in which case the terminology you used in not 'standard').
>>>
>>> 3. There are enough examples in 'rugarch.tests' folder in the source
>>> distribution, online blog examples, previous mailing list posts, other
>>> online resources, for you to be able to do what you need.
>>>
>>> Finally, I am more likely to respond to future requests for help if you
>>> provide minimally reproducible examples without sending zip files of your
>>> data (this is rarely needed), showed that you made an effort to read the
>>> documentation, and have signed your emails with your real name.
>>>
>>> Regards,
>>> Alexios
>>>
>>>
>>> On 08/05/2013 11:28, Neuman Co wrote:
>>>>
>>>>
>>>> I mean, I only try to get the one-step ahead in-sample predictions. So
>>>> I do NOT want to leave out any observations in the estimation stage? I
>>>> want to use all observations, estimate the GARCH and use the estimated
>>>> parameters and data to get one step ahead in sample predictions so I
>>>> can use these one-step-ahead-in-sample predictions of my cond.
>>>> volatility and cond. mean to calculate the VaR.
>>>>
>>>> 2013/5/8 Neuman Co <neumancohu at gmail.com>:
>>>>>
>>>>>
>>>>> Also
>>>>> http://www.unstarched.net/2013/02/27/whats-new-in-rugarch-ver-1-01-5/
>>>>> does not work if I try it.
>>>>> If I do
>>>>> c(is(sigma((fit))), is(fitted(fit)), is(residuals(fit)))
>>>>> I do not get xts xts xts but numeric vector and so on?
>>>>>
>>>>> If I try
>>>>> plot(xts(fit at model$modeldata$data, fit at model$modeldata$index),
>>>>> auto.grid = FALSE,
>>>>>       minor.ticks = FALSE, main = 'S&P500 Conditional Mean')
>>>>> lines(fitted(fit), col = 2)
>>>>> grid()
>>>>>
>>>>> I get the error messages
>>>>> Fehler in plot(xts(fit at model$modeldata$data,
>>>>> fit at model$modeldata$index),
>>>>> :
>>>>>     Fehler bei der Auswertung des Argumentes 'x' bei der
>>>>> Methodenauswahl
>>>>> für Funktion 'plot': Fehler in xts(fit at model$modeldata$data,
>>>>> fit at model$modeldata$index) :
>>>>>     order.by requires an appropriate time-based object
>>>>>
>>>>> and sigma(f) is also not working?
>>>>> Fehler in UseMethod("sigma") :
>>>>>     nicht anwendbare Methode für 'sigma' auf Objekt der Klasse
>>>>> "c('uGARCHforecast', 'GARCHforecast', 'rGARCH')" angewendet
>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>>
>>>>> I just tried to understand the examples, but they do not work?
>>>>>
>>>>> 2013/5/8 Neuman Co <neumancohu at gmail.com>:
>>>>>>
>>>>>>
>>>>>> The data I am working with can be found here:
>>>>>> http://uploadeasy.net/upload/2fvhy.rar
>>>>>>
>>>>>> I fitted the following model:
>>>>>> alvnomodel<-ugarchspec(variance.model = list(model = "sGARCH",
>>>>>> garchOrder = c(1, 1)),
>>>>>> mean.model = list(armaOrder = c(0, 0), include.mean = FALSE),
>>>>>> distribution.model = "norm")
>>>>>>
>>>>>> alvnomodelgarch<-ugarchfit(spec=alvnomodel,data=alvlloss)
>>>>>>
>>>>>> Now I want to get the one-day ahead forecasts of the cond. volatility
>>>>>> and the cond. mean. I try to applay ugrachforecast:
>>>>>>
>>>>>> ugarchforecast(alvnomodelgarch, n.ahead = 1,out.sample=50,n.roll=10)
>>>>>>
>>>>>> But I get the error message:
>>>>>> ugarchforecast-->error: n.roll must not be greater than out.sample!
>>>>>>
>>>>>> What is wrong?
>>>>>>
>>>>>> Also I don't know what values I should take for out.sample and n.roll?
>>>>>> I just want to get 1 day ahead forecasts. What values do I need to
>>>>>> insert?
>>>>>>
>>>>>> 2013/5/7 alexios ghalanos <alexios at 4dscape.com>:
>>>>>>>
>>>>>>>
>>>>>>> Applying 'sigma' (conditional volatility) and 'fitted' (conditional
>>>>>>> mean)
>>>>>>> METHODS on a uGARCHforecast object will return the forecast values of
>>>>>>> those
>>>>>>> quantities with appropriately labelled dates (the T+0 time). This too
>>>>>>> is
>>>>>>> documented in the help files, and there was also a blog post about
>>>>>>> this
>>>>>>> ('Whats new in rugarch (ver 1.01-5)').
>>>>>>>
>>>>>>> For VaR, as I already mentioned, you can use the 'quantile' method on
>>>>>>> any of the returned S4 class objects.
>>>>>>>
>>>>>>> -Alexios
>>>>>>>
>>>>>>>
>>>>>>> On 07/05/2013 12:51, Neuman Co wrote:
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> thanks a lot for your help, but
>>>>>>>> "Use the 'sigma' and 'fitted' methods"
>>>>>>>>
>>>>>>>> But these are the fitted values for the volatility and the final
>>>>>>>> fitted values. But to calculate the VaR I need the 1 step ahead
>>>>>>>> forecast of the cond. sigmas and the 1 step ahead forecast of the
>>>>>>>> cond. mean. The cond.mean is not equivalent to the fitted values?
>>>>>>>> And
>>>>>>>> the fitted values are not one step ahead forecasts?
>>>>>>>>
>>>>>>>> 2013/5/7 alexios ghalanos <alexios at 4dscape.com>:
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Hello,
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> On 07/05/2013 12:15, Neuman Co wrote:
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I am using the rugarch package in R and I have some questions:
>>>>>>>>>>
>>>>>>>>>> I want to use the rugarch package to calculate the VaR.
>>>>>>>>>>
>>>>>>>>>> I used the following code to to fit a certain model:
>>>>>>>>>>
>>>>>>>>>> spec2<-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))
>>>>>>>>>>
>>>>>>>>>> model2<-ugarchfit(spec=spec2,data=mydata)
>>>>>>>>>>
>>>>>>>>>> Now I can look at the 2.5 % VaR with the following command:
>>>>>>>>>> plot(model)
>>>>>>>>>>
>>>>>>>>>> and choosing the second plot.
>>>>>>>>>>
>>>>>>>>>> Now my first question is: How can I get the 1.0% VaR VALUES, so
>>>>>>>>>> not
>>>>>>>>>> the plot, but
>>>>>>>>>> the values/numbers?
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Use the 'quantile' method i.e. 'quantile(model2, 0.01)'...also
>>>>>>>>> applies to
>>>>>>>>> uGARCHforecast, uGARCHsim etc It IS documented.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> In case of the normal distribution, one can easily do the
>>>>>>>>>> calculation of
>>>>>>>>>> the VaR with using the forecasted conditional volatility and the
>>>>>>>>>> forecasted
>>>>>>>>>> conditional mean:
>>>>>>>>>>
>>>>>>>>>> I use the ugarchforecast command and with that I can get the cond.
>>>>>>>>>> volatility
>>>>>>>>>> and cond. mean (my mean equation is an modified ARMA(5,5), see
>>>>>>>>>> above
>>>>>>>>>> in
>>>>>>>>>> the spec
>>>>>>>>>> command):
>>>>>>>>>>
>>>>>>>>>> forecast = ugarchforecast(spec, data, n.roll = , n.ahead = ,
>>>>>>>>>> out.sample=)
>>>>>>>>>>
>>>>>>>>>> # conditional mean
>>>>>>>>>> cmu = as.numeric(as.data.frame(forecast, which = "series",
>>>>>>>>>> rollframe="all", aligned = FALSE))
>>>>>>>>>> # conditional sigma
>>>>>>>>>> csigma = as.numeric(as.data.frame(forecast, which = "sigma",
>>>>>>>>>> rollframe="all", aligned = FALSE))
>>>>>>>>>>
>>>>>>>>> NO. 'as.data.frame' has long been deprecated. Use the 'sigma' and
>>>>>>>>> 'fitted'
>>>>>>>>> methods (and make sure you upgrade to latest version of rugarch).
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> I can calculate the VaR by using the property, that the normal
>>>>>>>>>> distribution
>>>>>>>>>> is part of the location-scale distribution families
>>>>>>>>>>
>>>>>>>>>> # use location+scaling transformation property of normal
>>>>>>>>>> distribution:
>>>>>>>>>> VaR = qnorm(0.01)*csigma + cmu
>>>>>>>>>>
>>>>>>>>>> My second question belongs to the n.roll and out.sample command. I
>>>>>>>>>> had
>>>>>>>>>> a look at the
>>>>>>>>>> description
>>>>>>>>>> http://www.inside-r.org/packages/cran/rugarch/docs/ugarchforecast
>>>>>>>>>> but I did not understand the n.roll and out.sample command. I want
>>>>>>>>>> to
>>>>>>>>>> calculate the
>>>>>>>>>> daily VaR, so I need one step ahead predicitons and I do not want
>>>>>>>>>> to
>>>>>>>>>> reestimate
>>>>>>>>>> the model every time step. So what does it mean "to roll the
>>>>>>>>>> forecast
>>>>>>>>>> 1 step " and
>>>>>>>>>> what is out.sample?
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> out.sample, which is used in the estimation stage retains
>>>>>>>>> 'out.sample'
>>>>>>>>> data
>>>>>>>>> (i.e. they are not used in the estimation) so that a rolling
>>>>>>>>> forecast
>>>>>>>>> can
>>>>>>>>> then be performed using this data. 'Rolling' means using data at
>>>>>>>>> time
>>>>>>>>> T-p
>>>>>>>>> (p=lag) to create a conditional 1-ahead forecast at time T. For the
>>>>>>>>> ugarchforecast method, this means using only estimates of the
>>>>>>>>> parameters
>>>>>>>>> from length(data)-out.sample. There is no re-estimation taking
>>>>>>>>> place
>>>>>>>>> (this
>>>>>>>>> is only done in the ugarchroll method).
>>>>>>>>> For n.ahead>1, this becomes an unconditional forecast.
>>>>>>>>> Equivalently,
>>>>>>>>> you
>>>>>>>>> can
>>>>>>>>> append new data to your old dataset and use the ugarchfilter
>>>>>>>>> method.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> My third question(s) is (are): How to calculate the VaR in case of
>>>>>>>>>> a
>>>>>>>>>> standardized
>>>>>>>>>> hyperbolic distribution? Can I still calculate it like in the
>>>>>>>>>> normal
>>>>>>>>>> case
>>>>>>>>>> or does it not work anymore (I am not sure, if the sdhyp belongs
>>>>>>>>>> to
>>>>>>>>>> the
>>>>>>>>>> location-scale family).
>>>>>>>>>>
>>>>>>>>>> Even if it does work (so if the sdhyp belongs to the family of
>>>>>>>>>> location-scale distributions) how do I calculate it in case of a
>>>>>>>>>> distribution, which does not belong to the location-scale family?
>>>>>>>>>> (I mean, if I cannot calculate it via VaR = uncmean + sigma*
>>>>>>>>>> z_alpha
>>>>>>>>>> how
>>>>>>>>>> do I have to calculate it). Which distribution implemented in the
>>>>>>>>>> rugarch
>>>>>>>>>> package does not belong to the location-scale family?
>>>>>>>>>>
>>>>>>>>> ALL distributions in the rugarch package are represented in a
>>>>>>>>> location-
>>>>>>>>> and
>>>>>>>>> scale- invariant parameterization since this is a key property
>>>>>>>>> required
>>>>>>>>> in
>>>>>>>>> working with the standardized residuals in the density function
>>>>>>>>> (i.e.
>>>>>>>>> the
>>>>>>>>> subtraction of the mean and scaling by the volatility).
>>>>>>>>> The standardized Generalized Hyperbolic distribution does indeed
>>>>>>>>> have
>>>>>>>>> this
>>>>>>>>> property, and details are available in the vignette. See also paper
>>>>>>>>> by
>>>>>>>>> Blaesild (http://biomet.oxfordjournals.org/content/68/1/251.short)
>>>>>>>>> for
>>>>>>>>> the
>>>>>>>>> linear transformation (aX+b) property.
>>>>>>>>>
>>>>>>>>> If working with the standard (NOT standardized) version of the GH
>>>>>>>>> distribution (\lambda, \alpha, \beta, \delta, \mu) you need to
>>>>>>>>> apply
>>>>>>>>> the
>>>>>>>>> location/scaling transformation as the example below shows which is
>>>>>>>>> equivalent to just using the location/scaling transformation in the
>>>>>>>>> standardized version:
>>>>>>>>> #################################################
>>>>>>>>> library(rugarch)
>>>>>>>>> # zeta = shape
>>>>>>>>> zeta = 0.4
>>>>>>>>> # rho = skew
>>>>>>>>> rho = 0.9
>>>>>>>>> # lambda = GIG mixing distribution shape parameter
>>>>>>>>> lambda=-1
>>>>>>>>> # POSITIVE scaling factor (sigma is in any always positive)
>>>>>>>>> # mean
>>>>>>>>> scaling = 0.02
>>>>>>>>> # sigma
>>>>>>>>> location = 0.001
>>>>>>>>>
>>>>>>>>> # standardized transformation based on (0,1,\rho,\zeta)
>>>>>>>>> # parameterization:
>>>>>>>>> x1 = scaling*qdist("ghyp", seq(0.001, 0.5, length.out=100), shape =
>>>>>>>>> zeta,
>>>>>>>>> skew = rho, lambda = lambda)+location
>>>>>>>>> # Equivalent to standard transformation:
>>>>>>>>> # First obtain the standard parameters (which have a mean of zero
>>>>>>>>> # and sigma of 1).
>>>>>>>>> parms = rugarch:::.paramGH(zeta, rho, lambda)
>>>>>>>>> x2 = rugarch:::.qgh( seq(0.001, 0.5, length.out=100), alpha =
>>>>>>>>> parms[1]/abs(scaling), beta = parms[2]/abs(scaling),
>>>>>>>>> delta=abs(scaling)*parms[3], mu = (scaling)*parms[4]+location,
>>>>>>>>> lambda
>>>>>>>>> =
>>>>>>>>> lambda)
>>>>>>>>> all.equal(x1, x2)
>>>>>>>>> # Notice the approximation error in the calculation of the quantile
>>>>>>>>> for #
>>>>>>>>> which there is no closed form solution (and rugarch uses a
>>>>>>>>> tolerance
>>>>>>>>> # value of .Machine$double.eps^0.25)
>>>>>>>>> # Load the GeneralizedHyperbolic package of Scott to adjust the
>>>>>>>>> # tolerance:
>>>>>>>>> library(GeneralizedHyperbolic)
>>>>>>>>>
>>>>>>>>> x1 = location+scaling*qghyp(seq(0.001, 0.5, length.out=100), mu =
>>>>>>>>> parms[4],
>>>>>>>>> delta = parms[3], alpha =  parms[1], beta = parms[2], lambda =
>>>>>>>>> lambda,
>>>>>>>>> lower.tail = TRUE, method = c("spline", "integrate")[2], nInterpol
>>>>>>>>> =
>>>>>>>>> 501,
>>>>>>>>> subdivisions = 500, uniTol = 2e-12)
>>>>>>>>> # equivalent to:
>>>>>>>>> x2 = qghyp(seq(0.001, 0.5, length.out=100), mu =
>>>>>>>>> (scaling)*parms[4]+location, delta = abs(scaling)*parms[3], alpha =
>>>>>>>>> parms[1]/abs(scaling), beta = parms[2]/abs(scaling), lambda =
>>>>>>>>> lambda,
>>>>>>>>> lower.tail = TRUE, method = c("spline", "integrate")[2], nInterpol
>>>>>>>>> =
>>>>>>>>> 501,
>>>>>>>>> subdivisions = 500, uniTol = 2e-12)
>>>>>>>>>
>>>>>>>>> all.equal(x1, x2)
>>>>>>>>> #################################################
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> Thanks a lot for your help!
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Regards,
>>>>>>>>>
>>>>>>>>> Alexios
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> _______________________________________________
>>>>>>>>>> R-SIG-Finance at r-project.org mailing list
>>>>>>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
>>>>>>>>>> -- Subscriber-posting only. If you want to post, subscribe first.
>>>>>>>>>> -- Also note that this is not the r-help list where general R
>>>>>>>>>> questions
>>>>>>>>>> should go.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>
>>>
>>
>



--
Neumann, Conrad