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

[Neuman Co]

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.
>>>>>>>>
>>>>>>>
>>>>>>
>>>>>
>>
>