[R-SIG-Finance] robust estimation of DCC GARCH model

[ahmed sedky]

I have developed a new method of robust  estimation of
DCC GARCH model but I have a problem in the simulation study which is how to
simulate data from multivariate contaminated normal distribution under some 
conditions 
Return data are generated using an underlying multivariate normal
distribution as defined by the DCC-GARCH in Engle(2002), 
1- a contaminated normal distribution with 5% contamination,
2- a contaminated normal distribution with 25% contamination.
The contaminated normal distributions are defined with the
following mixture of multivariate distributions
 et@(1-π) e1,t+ πe2,t ,                        e1,t~ 
N(0,1)    ,   e2,t~ N(0, σ2)
Where
π is a Bernoulli random variable with a probability equal to the percentage of
contamination and the simulation studies use σ =3
or 5 to make the standard deviation three or five  times  larger.
 
for
example: 
rcnorm
= function(nobs, mean=0, sd1=1, sd2=3, prob=0.25)
{sd
<- sample(c(sd1,sd2), nobs , replace=T,
                          Prob =c(1-prob,prob))
 rnorm(nobs, mean, sd)
}
 
These
contaminated normal distributions are standardized to have a variance equal to
1. 
 
A
data set with three assets has volatility parameters defined by a GARCH(1,1) as
 
a
<- c (0.10, 0.60, 0.32)
 
A
<- diag(c (0.25,0.11,0.14))
 
B
<- diag(c (0.58, 0.80, 0.71))
 
and
correlation parameters as                   
α = 0.25      , β =
0.70
dcc.para
<- c (0.25,0.70)
 
is
generated from each of the above mentioned distributions for over 1000 time
periods to create four sets of generated daily returns.
initial
unconditional correlation matrices, R_0, are used for each distribution
 
uncR
<- matrix(c(1.0, 0.80, 0.80, 0.80, 1.0, 0.80, 0.80, 0.80, 1.0),3,3)
 
which
describes a set of assets where all assets are closely related to each other.
This set of assets is selected because possible outliers in each asset may
impact all of the assets in the set. 
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