Im sorry but you need to think a little bit about what you are doing here.
How can your u be negative or greater than 1 ? Any CDF transformation (p*)
should return a set of probabilities [0,1].
Do you wonder why you get zillions of NA when you feed q* with anything other
than [0,1] bounded numbers?
Retrace your steps and think about what you are doing rather than mechanically
following a recipe.
-Alexios
On 28 May 2014, at 18:29, Guillaume PEALAT <guillaume.pea...@gmail.com> wrote:
> Alexios,
>
> Thanks.
> I thought about that but if I translate u back to z using the following
> function:
> u.1.sim = qspd(u.1, gpd.spx)
>
> I get zillions of NA.
>
> > head(u.1)
> [1] -1.19669066 1.86539169 0.41492263 0.07366442 -0.80536637 1.09567877
> > head(u.1.sim)
> [1] NA NA -0.1510786 -1.5404552 NA NA
>
> So there is still something wrong but I can not pinpoint it.
>
> Thanks
>
>
>
> 2014-05-28 18:18 GMT+01:00 alexios ghalanos <alex...@4dscape.com>:
> You've missed a step. Think about it:
> 1. You take z.
> 2. Fit an spd.
> 3. Transform it to U using pspd.
> 4. Fit a copula on U.
> 5. Sample from copula to generate u.
> 6. Need to translate u back to z (step 1) using the quantile function
> (qspd) and the estimated parameters from step 2.
>
> i.e. you've missed step 6.
>
>
> -Alexios
>
> On 28/05/2014 16:53, Guillaume PEALAT wrote:
> > Hi,
> >
> > I am fitting some SPD distributions to past returns and some Copula to
> > simulate the dependance.
> > I am struggling with the simulation part, as the returns I simulate a
> > clearly out of line after some time.
> >
> > I have attached some sample code in order to clarify the point.
> >
> > I first calibrate the SPD distribution on the past returns:
> >
> > #Calibrating the SPD distributioon the residuals of an ARMA+GARCH
> >
> > *spec.u1 = ugarchspec(mean.model=list(armaOrder=c(1,1)),
> > distribution="std")*
> >
> > *fit.u1 = ugarchfit(spec.u1, return.u1)*
> >
> > *z.u1= residuals(fit.u1, standardize=TRUE)*
> >
> > *gpd.u1 = spdfit(z.u1, upper=1. - tailFraction, lower=tailFraction)*
> >
> >
> > #Calibrating the SPD distributioon the residuals of an ARMA+GARCH
> >
> > *spec.u2 = ugarchspec(mean.model=list(armaOrder=c(1,1)),
> > distribution="std")*
> >
> > *fit.u2 = ugarchfit(spec.u2, return.u1)*
> >
> > *z.u2= residuals(fit.u2, standardize=TRUE)*
> >
> > *gpd.u2 = spdfit(z.u2, upper=1. - tailFraction, lower=tailFraction)*
> >
> >
> > Then, once we have all this set, we need to calibrate the Copula of our
> > choice
> >
> >
> > #Calibrate the Copula
> >
> > #We extract the residuals from the xts into a vector
> >
> > *res.u1 = as.vector(z.u1[,1])*
> >
> > *res.u2 = as.vector(z.u2[,1])*
> >
> > #We transform the margin to uniform
> >
> > *U.u1 = pspd(res.u1, gpd.u1)*
> >
> > *U.u2 = pspd(res.u2, gpd.u2)*
> >
> >
> >
> > #We create the matrix to help us calibrate the Copula
> >
> > *test <-list()*
> >
> > *test[[1]] = U.u1*
> >
> > *test[[2]] = U.u2*
> >
> > *test_matrix = do.call(rbind, test)*
> >
> >
> >
> > *set.seed(123)*
> >
> >
> >
> > #We define the Copula we want to use
> >
> > *tcopula<-tCopula(param=0.5, dim=2, dispstr = "ex", df =6)*
> >
> > #We fit the Copula with maximum Likelihood
> >
> > *fit.mpl <- fitCopula(tcopula, t(test_matrix), method="ml")*
> >
> >
> >
> > #We get back the parameters
> >
> > #Rho
> >
> > *rho.fit = fit.mpl@copula@parameters[1]*
> >
> > #Degrees of Freedom
> >
> > *df.fit = fit.mpl@copula@parameters[2]*
> >
> >
> >
> > #Create fitted t-copula object
> >
> > *t.cop.fit = tCopula(param=rho.fit, dim=2, df=df.fit)*
> >
> >
> >
> > *margins = c("t", "t")*
> >
> > *paramMargins = list(list(df=df.fit),list(df=df.fit))*
> >
> >
> >
> > #Create fitted custom distribution object
> >
> > *myBvd.tcop.fit = mvdc(copula=t.cop.fit, margins = margins, paramMargins=
> > paramMargins)*
> >
> >
> >
> > If all is well, I should be able to run some simulations and simulate my
> > returns from this set up:
> >
> >
> > #Generate random numbers from the Copula
> >
> > *u = rMvdc(nsim, myBvd.tcop.fit)*
> >
> > *u.1 = u[,1]*
> >
> > #Generate the simulated returns
> >
> > *sim.u1 = ugarchsim(fit.u1, n.sim=nsim, startMethod="sample", m.sim=1,*
> >
> > * custom.dist=list(name="sample",distfit=matrix(u.1,
> > ncol=1)))*
> >
> > #Get back the simulated returns
> >
> > *sim.u1.returns = sim.u1@simulation$seriesSim*
> >
> >
> >
> > The problem lies in the order of magnitude the simulated returns. I can get
> > some occurrence of +26% for example, which is clearly wrong.
> >
> >
> > Could someone point me on the wrong part?
> >
> > I have also a remaining question:
> >
> > In the univariate case, we can simulate the random number with *rspd(n =
> > days, gpd.u1)*, and they will be in accordance with the gpd distribtuion
> > calibrated.
> >
> > In the multivariate case, can I consider this step to be taken care of by
> > the random number of the Copula since it has been calibrated on the margins
> > transformed to Uniform by the gpd distribution function?
> >
> >
> > Thanks
> >
> > [[alternative HTML version deleted]]
> >
> > _______________________________________________
> > R-SIG-Finance@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-finance
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> > -- Also note that this is not the r-help list where general R questions
> > should go.
> >
> >
>
>
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