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rugarch and copulas

9 messages · ludovic.theate, Alexios Ghalanos

Original
ludovic.theate
# 
Thanks for your answer, and sorry for the long delay.

OK, I am now giving a try to this cgarchfit function. However, as I can see,
it works only (for the moment) with Gaussian and t-copulas. But I would like
to have access to a more complete panoply of copulas models, including
nested-archimedean copulas (even vines if time permits). So I am still
interested to know how I could specify the innovations in the Garch
prediction function of the rugarch package ?

Thanks for your help.



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Alexios Ghalanos
# 
1. Open the source package and see how the normal and student models are used in combination with GARCH...that should provide you with an idea of how to combine the two.
2. Read the vignette which contains additional details on the models with additional references.
3. Search this forum for an old reply to a similar question.

-Alexios

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On Nov 8, 2012, at 13:43, "ludovic.theate" <ludovic.theate at gmail.com> wrote:

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      ludovic.theate
    

    

      
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Alexios,

Thanks for your reply.

Unfortunately, I do not have so much time to spend on this problem and as I
see, the rmgarch package has become quite complex. So I think I will
continue for the moment using the fgarch package which is more accessible
and would provide me an easier way to deal with other copulas than the
elliptic one.

However, I will of course keep an eye on your package and I am looking
forward to being able to use the cgarchsim function with other copulas, e.g.
archimedean copulas.

Thanks again,

Regards,

Ludovic



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      ludovic.theate
    

    

      
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Hi Alexios,

Things are often clearer in the morning, and I think I changed a little bit
my mind about what I said yesterday. I really do not like the fgarch
package, since there is no well defined link between the fit and the
simulation methods. I clearly prefer the architecture spec -> fit -> sim you
use in rugarch.

So I decided to give another try, and I just would like to ask to you (and
of course the other people following this list) if you could approve/amend
the following approach :

1)	I filter the data using an univariate rugarch model for each currency I
am modelling.
2)	I evaluate the standardized residuals using ?residuals(fit)/sigma(fit)?
as explained in a previous threat.
3)	I transform them into uniform using either the ranks, or using a
parametric approach you described in the thread I was talking about.
Unfortunately, I am not sure I understand your explanation (?extracting any
conditional higher moment parameters from the GARCH fitted object and pass
those with the standardized residuals to the "pdist" function of rugarch
indicating the distribution used?). Could you explain with a little more
details please ?
4)	With this matrix of uniform marginals, I am able to fit the copulas I am
interested in (even nested, or vine ones), compare them, make tests, and
choose the most appropriate one.
5)	Using this copula, I can generate a random n_currencies x n_simulations x
n_horizon matrix containing the innovations.
6)	Then, if I?ve correctly understood, I can simply plug each row (for each
currency) of this matrix inside the ? custom.dist = list(name = NA, distfit
= NA) ? option of ugarchsim and simulate the trajectories. Is it correct ?
If I made this for each currencies, I will get correlated sample
trajectories.

Do you think this kind of algorithm is correct ? Once again, thanks for your
help.

Regards,

Ludovic




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      Alexios Ghalanos
    

    

      
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Hi,

1. ok, you fit a GARCH model to each series (filter in rugarch means
you supply a pre-defined set of parameters without fitting).

2. Since version 1.0-12., you can use residuals(fit, standardize = 
TRUE). R-forge has 1.0-13 which is more up to date.

3. You have 3 choices for the transformation:
a. Empirical (ranks) -> Genest 1985 (Pseudo-Likelihood),
b. Semi-Parametric -> Davison and Smith (1990) (e.g. spd package),
c. Parametric -> Joe (1987) (Inference-Functions-for-Margins).
The rmgarch vignette contains details on the methods and relevant 
references.

 >args(pdist)
function(distribution = "norm", q, mu = 0, sigma = 1, lambda = -0.5,
     skew = 1, shape = 5)

Since you are passing (0,1) residuals, mu=0 and sigma = 1, but depending 
on what conditional distribution you used to fit the univariate GARCH 
models you will need to provide the additional parameters
e.g. from the "coef(fit)" you will have a shape and skew parameter if 
you fitted a distribution which has these parameters.

You will likely also find the code below useful once you have 
transformed your residuals into uniform variates:

# make tail adjustments in order to avoid problem with the quantile
# functions in optimization
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
}


4./5 Correct

6. Incorrect. You first need to do a "reverse-transform" of the copula 
simulated values by using the qdist (quantile) function. THEN you plug 
in to the custom.dist function. These are now dependent (in the cross 
section) standardized residuals.

Note that this topic was also covered here:
http://r.789695.n4.nabble.com/Copula-in-R-td928826.html

As to the correctness of this approach, I would say it is a valid 
method, which adopts a 2/3 stage compromise rather than a full 1-stage 
ML approach which would be computationally forbidding. In the rmgarch
package, things are done slightly differently since the focus is on
using DCC based modelling with elliptical copulas (although the non-DCC
approach is also allowed).

Hope that clarifies.

-Alexios

        
On 09/11/2012 10:29, ludovic.theate wrote:

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      ludovic.theate
    

    

      
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Hi Alexios,

It is really better than just clarification, your help is really precious
and appreciated. Thanks.

Just a remark concerning point 5. It was just a lack of precision from my
side, since in the actual version of the model, I am already using the
command

copulaSpec <- mvdc(calibration$t.copula, calibration$models,sstdSpec)

to do what you call the "reverse-transform".

In a (near ?) future, I plan to try to understand all these multivariate
models you are providing in your rmgarch package (especially the DCC ones),
but for the moment, I will deal only with copula-garch models.

Once again, thank you very much, and have a nice weekend,

Ludovic



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11 days later

    

      
      

        


  

        

      ludovic.theate
    

    

      
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Alexios,

Sorry but I've got a last problem.

I firstly simulated independant trajectories of my processes, and I find
acceptable results.

Then I tried to simulate correlated trajectories using the following
function (as we discussed last week) :

##########################
# Sim_Cop_Garch Function #
##########################


sim_cop_garch <- function(mfit,cop,nsim,horizon){
ncur = length(mfit)

result <- NULL
for(j in 1:nsim){

# Simulation of nsim random values of the copulas: these are uniform
#uni_res <- rCopula(horizon,cop)  # FIRST TRY
uni_res <- matrix(runif(horizon*ncur),ncol=ncur,nrow=horizon)  # SECOND TRY

# Inverse-transform : uniform values are transformed into appropriate values
(e.g. norm, sstd,...)
innov = matrix(NA, ncol = ncur, nrow = horizon)
for(i in 1:ncur){
	gdist = mfit[[i]]@model$modeldesc$distribution
	lambda = ifelse(mfit[[i]]@model$modelinc[18]>0,
mfit[[i]]@fit$ipars["ghlambda",1], 0)
	skew = ifelse(mfit[[i]]@model$modelinc[16]>0,
mfit[[i]]@fit$ipars["skew",1],  0)
	shape = ifelse(mfit[[i]]@model$modelinc[17]>0,
mfit[[i]]@fit$ipars["shape",1],  0)
	innov[,i] = qdist(gdist,uni_res[,i] , mu = 0, sigma = 1, lambda = lambda,
skew = skew, shape = shape)}

# Simulation of the ARIMA-GARCH model using the previously generated
innovations

one_simul <- matrix(NA,ncol=ncur,nrow=1)
for(i in 1:ncur){

test <- ugarchsim(mfit[[i]],n.sim=horizon,m.sim=1,
custom.dist=list(name="sample",distfit=matrix(innov[,i],ncol=1,nrow=horizon)))@simulation$seriesSim[horizon,1] 

one_simul[,i] <- exp(diffinv(test))[2] }

result <- rbind(result,one_simul)
}
return(result)
}


The results I got for a Gaussian copula were clearly incorrect. So I
modified the function to skip the copula-generated uniform random numbers
(with the "first try" comment ) and I used the runif method instead. (with
the "second try" comment)  Even when I do this, I find impossible results,
so the problem doesn't come from the copula.

I think I have maybe misunderstood the behavior of the custom.dist option in
the ugarchsim method. Could you please have a look and tell me if you see
something wrong ? Thanks a lot.

Kind regards,

Ludovic



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      Alexios Ghalanos
    

    

      
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This is not really a reproducible example...nevertheless, I am guessing 
you are trying to generate the final point of the path at 
simulation_time "horizon".
What you are forgetting is that the values in "simulation$seriesSim" are 
returns, so doing "exp(diffinv(test))[2]" on the last value (horizon) is 
meaningless. What you want (probably) is:

... at simulation$seriesSim[1:horizon,1]
one_simul[,i] <- tail(exp(diffinv(test)), 1)

-Alexios

        
On 21/11/2012 09:27, ludovic.theate wrote: