Thanks for your quick reply!
Then this should be the answer, isnt it?
# Calcualte the Expected Shortfall (99)
test_es = apply(df1_var, 1, function(x) x['Mu'] + x['Sigma'] *
((integrate(f, 0, 0.01, skew =
x['Skew'], shape = x['Shape'])$value) / (0.01)))
Greetings
Daniel
2013/6/19 Alexios Ghalanos <[email protected]>
> From a quick look at your code (am not at my computer), you have forgotten
> to divide the integration result by the coverage rate (see rugarch::ESTest
> for an example of the calculation).
>
> Regards,
> Alexios
>
> Sent from my iPad
>
> On 19 Jun 2013, at 09:47, Daniel Liebert <[email protected]>
> wrote:
>
> > Hi all,
> > Iam trying to compute the Expected Shortfall from a GARCH(1,1) with sged
> > innovations created via the great rugarch package. The problem is that
> the
> > range of values compared to the VaR(99) is totally different and I dont
> > know where I have made the mistake.
> > Here is my code:
> >
> > library(quantmod)
> > library(rugarch)
> > library(parallel)
> > library(PerformanceAnalytics)
> >
> > # get Data
> > mmm <- getSymbols("MMM", from = "2005-01-01", to = "2013-05-31")
> > mmm <- Ad(get(mmm))
> > ldr_mmm <- Return.calculate(mmm, method = "log"
> > # remove NA observations
> > ldr_mmm <- na.omit(ldr_mmm)
> >
> > ctrl = list(rho = 1, delta = 1e-9, outer.iter = 1000, tol = 1e-7) #
> options
> > for solver
> > cl = makePSOCKcluster(10) # Create a Parallel Socket Cluster
> >
> > # Choosing estimation and test window
> > n_all_mmm = nrow(mmm)
> > n_test_mmm <- nrow(as.xts(ldr_mmm)["2007-01-04/2013-05-31"]) # testing
> > window
> > n_est_mmm <- n_all_mmm - n_test_mmm # estimation window
> >
> > # Fitting a GARCH(1,1) Model with skewed generalized error distribution
> > innovations
> > fit_MMM_def = ugarchspec(variance.model = list(model = "sGARCH",
> garchOrder
> > = c(1,1)),
> > mean.model = list(armaOrder =
> > c(0,0), include.mean = TRUE),
> > distribution.model = "sged")
> >
> > # Calcualte Backtest
> > MMM.backtest = ugarchroll(fit_MMM_def, data = ldr_mmm, n.ahead = 1,
> > forecast.length =
> > n_test_mmm, refit.every = 20, refit.window = "moving",
> > solver = "hybrid",
> > fit.control = list(), solver.control = ctrl,
> > calculate.VaR = TRUE,
> > VaR.alpha = c(0.01), # Compute VaR = TRUE
> > cluster = cl)
> >
> > # Calculate the VaR(99) by your own if calculate.VaR = FALSE @ ugarchroll
> > df1_var <- as.data.frame(MMM.backtest, which = "density")
> > f = function(x, skew, shape) qdist("sged", p = x, mu = 0, sigma = 1,
> skew =
> > skew, shape = shape)
> > test_var = df1_var[, 'Mu'] + qdist("sged", 0.01, 0, 1, skew = df1_var[,
> > 'Skew'],
> > shape =
> > df1_var[, 'Shape']) * df1_var[, 'Sigma']
> >
> > # Lets compare it with the results from the ugarchroll function
> > MMM_GARCH <- MMM.backtest@forecast
> > head(cbind(test_var, as.data.frame(MMM_GARCH[["VaR"]]))) # exactly the
> > same, thats good!
> >
> > # Calcualte the Expected Shortfall (99)
> > test_es = apply(df1_var, 1, function(x) x['Mu'] + x['Sigma'] *
> integrate(f,
> > 0, 0.01, skew = x['Skew'], shape = x['Shape'])$value)
> > test_es <- as.zoo(as.xts(test_es))
> > test_es <- aggregate(test_es, function(tt) as.Date(tt, tz = "")) #convert
> > to date
> >
> > # Lets compare the VaR(99) and the ES(99)
> > layout(1:2)
> > plot(test_es) # ES(99)
> > plot(as.zoo(MMM.backtest@forecast$VaR[1])) # VaR(99)
> >
> > The most of the ideas are from http://www.unstarched.net (rugarch). My
> clue
> > is that the integration is wrong but Iam not sure...
> >
> > Thanks in advance
> > Daniel
> >
> > [[alternative HTML version deleted]]
> >
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>
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