Hello,
I am trying to use the R packages rugarch and VineCopula for simulating returns
of 112 companies for a time period of 25 days with daily re-estimations. After
the simulation, I wish to calculate the 99% and 95% value-at-risk and compare
them to the actual returns.I use a moving window of 250 days and 1000
simulations per iteration.
(This estimation is quite time-intensive as 112 companies might be too many for
VineCopula..)
The overall loop takes around 8 hours on my home computer, so I wouldn�t
recommend to actually run the code. My problem is that some of my calculated
value at risk forecasts seem to be positive � this is not a �just invert the
VaR� kind of problem (at least I don�t think so).
To summarize the code:
1. Fit GARCH models to each series.2. Extract standardized returns (and shape
parameters)3. Transform standardized returns to uniform marginals using
parametric method (IFM by Joe, 1987).4. Fit vine copulas5. Generate a 1000 x
112 matrix (1000 1-day ahead forecasts for all 112 companies)6. Reverse
transform the simulated values.7. Use these transformed forecasts in ugarchsim
8. Extract forecasted values & sigmas.9. Calculate Value-at-Risk.
Anyway, here�s my code so far:# Load Data and define variables
returns <- read.zoo("E:/Dropbox/my own/Programming/R/returns.csv",
header=TRUE, sep=",",
format="%d-%m-%y")model<-ugarchspec(variance.model=list(model="sGARCH",garchOrder=c(1,1)),mean.model=list(armaOrder=c(1,0),include.mean=FALSE),distribution.model="ged")times
<- as.data.frame(time(returns))windows <- matrix(0, 112, 250)familyset <-
c(1:5, 7, 10, 13, 14, 17, 20) # The vine copulas to be
testedsim <- array(0, dim = c(1000, 112))residuals2 <- array(0, dim = c(1000,
112))rvine_fitted <- array(0, dim = c(25,1000,112))rvine_sigma <- array(0, dim
= c(25,1000,112))VaR01 = VaR05 = array(0, dim = c(25,1000,112))
#Main calculation
for(i in 1:25){ print(i) windows <- window(returns_crisis,
start=times[376-250-24+i,1], end=times[376-25+i,1]) #Define the
moving window fit <- lapply(windows, ugarchfit, spec=model, solver="hybrid")
#Fit the garch
models print("rugarch fitting done") residuals <- sapply(fit, residuals,
standardize=TRUE)
#Extract residuals & shape parameters shape <-
sapply(fit, coef) shape <- shape[5,] UniformResiduals <- pged(residuals, nu =
shape)
#Transform residuals into uniform marginals
if(any(UniformResiduals > 0.99999)) { ix = which(UniformResiduals >
0.99999) UniformResiduals [ix] = 0.99999 } if(any(UniformResiduals <
.Machine$double.eps)) { ix = which(UniformResiduals <
(1.5*.Machine$double.eps)) UniformResiduals [ix] = .Machine$double.eps }
rvine <- RVineStructureSelect(UniformResiduals, indeptest=TRUE,
familyset=familyset) #Fit the Vine copulas print(paste(i,"RVine
fitting done")) for(j in 1:1000)
#Simulate 1000 1-day ahead using VineCopula
{ sim[j,] <- RVineSim(1, rvine)
# 1000 x 112 matrix of forecasts }print(paste(i,"RVine simulation done"))
for(k in 1:112)
#Next: ugarchsimulation for all 112 companies
{ residuals2[,] <- qged(sim[,], nu = shape[k])
# 1000 x
112 matrix of standardized residuals residuals_temp <-
residuals2[,k]
# 1000 x 1 vector of standardized
residuals for individual company rvine_sim <-
ugarchsim(fit[[k]], n.sim=1, m.sim=1000, custom.dist = list(name=NA,
distfit=residuals_temp)) #1000 simulations using the standardized residuals
from Vine copula models for ugarchfit rvine_fitted[i,,k] <-
fitted(rvine_sim)
#Extract forecasted values - 25 x 1000 x
112 rvine_sigma[i,,k] <- sigma(rvine_sim)
#Extract forecasted sigmas - 25 x 1000 x 112 for(j in 1:1000)
#Next: Value at risk { VaR01[,j,k] <-
rvine_fitted[,j,k] + rvine_sigma[,j,k] * qdist('ged', 0.01, mu=0, sigma=1,
shape = shape[k]) #Value at risk for 99% quantile VaR05[,j,k] <-
rvine_fitted[,j,k] + rvine_sigma[,j,k] * qdist('ged', 0.05, mu=0, sigma=1,
shape = shape[k]) #Value at risk for 95% quantile }
}}remove(i, j, k)
#Cleanupremove(windows, fit, residuals, shape,
residuals2, residuals_temp, rvine, sim, rvine_sim) #Cleanup Hope I
didn�t make any mistakes in my approach, but it seems like this is the
�standard� copula + rugarch approach � if anyone is familiar with this, I am
open to suggestions on how to speed up the simulations.
So far, so good � the problem I am facing now:
Some (only a few) of my value at risk values are positive..I have manually
checked and it seems like the fitted value is much larger than the sigma, so
Value at Risk is positive � which doesn�t really make any economic sense to me.
Here�s a dropbox link to the returns.csv, in case anyone is interested in
running my code: https://www.dropbox.com/s/69i5959f3h4kweb/returns.csv
Best Regards,
Ole
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