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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