# [R] DCC model estimation with t-Student distribution rmgarch

Tommaso Ferrari tom|err|93 @end|ng |rom gm@||@com
Thu Aug 22 14:55:43 CEST 2019

```Dear all,
I was analyzing and implementing the DCC model (Dynamic Conditional
Correlation) for the one-day forecast calculation of the
variance-covariance matrix of a system consisting of, approximately,
30 stocks. For each title I consider a historical series of logarithmic
daily returns of 250 samples.
In particular, I was interested in the simulation of this model using the
t-Student distribution.
In this regard I was using the "rugarch" and "rmgarch" packages.
According to the examples found in the literature, I run my analysis in the
following way:

1) specification of the univariate garch model for each stock passing the
number of degrees of freedom of the t-Student distribution as input
(parameter mshape)

2) multifitting of the univariate garch models

3) specification of DCC model with a multivariate t-Student distribution
(degrees of freedom are not passed as input, in this case)

4) fitting of the DCC model

5) variance-covariance matrix forecasting

I give an example of the code I'm running (qxts is the time series data,
mshape is the number of degrees of freedom):

# GARCH(1,1) specification
garch11.spec = ugarchspec(mean.model = list(armaOrder = c(0, 0)),
variance.model = list(garchOrder = c(1, 1), model = "sGARCH"),
distribution.model = "std", fixed.pars = list(shape = mshape))
# replicate Garch(1,1) spec for both time series
uspec = multispec(replicate(ncol(qxts), garch11.spec))
# Fit Garch models: hybrid -> in case of non convergence, all solvers are
used
multf = multifit(uspec, qxts, solver = "hybrid", fit.control = list(scale =
1))
# Dcc model spec
dcc.garch11.spec = dccspec(uspec = uspec, dccOrder = c(1, 1), distribution
= "mvt", model = "DCC")
# Fitting parameters of DCC
dcc.fit = dccfit(dcc.garch11.spec, qxts, fit = multf, fit.control =
list(scale = TRUE))
# dcc.fit = dccfit(dcc.garch11.spec, qxts, fit = multf, fit.control =
list(scale = 1))
# Forecast
dcc.fcst = dccforecast(dcc.fit, n.ahead = 1)
varmat = rcov(dcc.fcst)[[dt_cov]][,, 1]

However, using a number of degrees of freedom of 2.5, I get the following
error:

Error in solve.default(A) : system is computationally singular: reciprocal
condition number = 1.19994e-18

If, for example, I change the degrees of freedom from 2.5 to 2.6, the error
no longer appears.
I would like to know if there is a way to allow the calculation to be
performed even using a number of degrees of freedom equals to 2.5, as I
cannot find any reference in the literature that addresses this problem.

I also tried the following idea.
I don't pass the number of degrees of freedom as input, but I make sure
that, for each title, the number of degrees of freedom is calculated
internally by the function multifit.
Obviously, I get different degrees of freedom depending on the stock
considered.
In this case, however, passing the calculated parameters of the multifit to
the dccfunction, leads to the following error:
'data' must be of a vector type, was 'NULL'
even if the data sample I pass as input contains no null value.

I would like to know if these problems are due solely to the numerical
values of the data passed as input or if I am conceptually wrong in the
implementation of the method.

Thanks to all

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