Using Copula Innovations in GARCH Simulation

Summary

The document asks how to drive a fitted asymmetric GARCH model with innovations generated from a copula fitted to residuals for two stocks. The model includes an autoregressive moving-average mean, skewed Student-t innovations, and fixed parameter values. The proposed simulation call passes a vector of copula-generated innovations through a custom distribution argument.

The reported error and warnings indicate that the interface is receiving an improperly structured custom distribution object: the function checks for a distribution name and fit object, but the example supplies a vector as the name and leaves the fit entry absent. The document provides no accepted implementation or resolved answer, so it does not establish how to pass precomputed innovations correctly or whether the fitted marginal distributions and copula dependence are preserved. Its value is mainly in identifying the challenge of combining marginal volatility dynamics with cross-asset dependence during simulation.

Key ideas

• The question concerns simulating multiple GARCH processes with dependence modeled through copula innovations.
• The example uses an asymmetric GARCH specification with an ARMA mean and skewed Student-t errors.
• The custom distribution argument appears to expect structured fields rather than a raw innovation vector.
• The posted error suggests required distribution metadata is missing or malformed.
• The document does not provide a working fix or validate a simulation method.

Tags

# simulating from GARCH model with copula innovations


# simulating from GARCH model with copula innovations












I have a GARCH model fitted on stock returns as:

```
spec=ugarchspec(variance.model=list(model="eGARCH", garchOrder=c(1,1)),
                mean.model=list(armaOrder=c(2,4), include.mean=TRUE), distribution.model="sstd",
                fixed.pars=list(mu=-0.0005079, ar1= -0.8562921,ar2=-0.9857075, ma1=0.8959524,ma2=0.9844128,ma3=0.0007078,
                                ma4=-0.0387716,omega=-0.0520487, alpha1=-0.0070554, beta1=0.9928413,gamma1=0.1154331,
                                shape=8.2996960,skew=2))
```

I have also filled a copula on two stocks (residuals from the GARCH) from which I simulate innovations with the copula dependence structure. I now want to use the innovations to feed in the GARCH model. Rugarch docs shows that I can do it with the `ugarchspec` method using the `custom.dist` option as shown

```
path1 <- ugarchpath(spec, n.sim=2800, n.start=1, m.sim=1, custom.dist = list(name=sim_4))
```

I am inputting `sim_4` as a vector of innovations and getting the error:

```
path1 <- ugarchpath(spec, n.sim=2800, n.start=1, m.sim=1, custom.dist = list(name=sim_4))
Error in if (is.na(custom.dist$name) | is.na(custom.dist$distfit)[1]) { : 
  missing value where TRUE/FALSE needed
In addition: Warning messages:
1: In is.na(custom.dist$distfit) :
  is.na() applied to non-(list or vector) of type 'NULL'
2: In if (is.na(custom.dist$name) | is.na(custom.dist$distfit)[1]) { :
  the condition has length > 1 and only the first element will be used
```

I am using the `rugarch` library... anyone can help?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.