Use This:
test_es = df1_var['Mu'] + df1_var['Sigma']*apply(df1_var, 1, function(x)
integrate(f,0,0.01, skew = x['Skew'], shape = x['Shape'])$value/0.01)
Best,
Alexios
On 19/06/2013 11:31, Daniel Liebert wrote:
Thanks for your quick reply!
Then this should be the answer, isnt it?
# Calcualte the Expected Shortfall (99)
test_es = apply(df1_var, 1, function(x) x['Mu'] + x['Sigma'] *
((integrate(f, 0, 0.01, skew =
x['Skew'], shape = x['Shape'])$value) / (0.01)))
Greetings
Daniel
2013/6/19 Alexios Ghalanos <[email protected]
<mailto:[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]
<mailto:[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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