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

[Neuman Co]

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
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>>>>>> -- Also note that this is not the r-help list where general R questions
>>>>>> should go.
>>>>>>
>>>>>
>>>>
>>>