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

[Neuman Co]

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
>>>>>
>>>>>
>>>>> _______________________________________________
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>>>>>
>>>>
>>>
>>