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

[alexios ghalanos]

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