Question: I want to generate an EGARCH process. My problem is that I do not see how to create new processes beyond those available.

The process itself is :

$$\epsilon(t) = \sigma(t) \eta(t)$$

$$\log(\sigma(t)^2 ) = w + b\log(\sigma(t-1)^2) + c\eta(t-1) + d \lvert\eta(t-1)\rvert$$

Notice that I want to use `RandomFunction` to generate the simulated values.

Then I'd like to estimate it using the `EstimatedProcess` to estimate the parameters. I want to experiment with false models..

Answer: 
From PlatoManiac's comments:

You could try [Verbeia's notebook](http://www.verbeia.com/mathematica/mma/gen_timeseries.nb), and replace `AppendRows[a,b]` with `Join[a,b,2]` and `ZeroMatrix` using `ConstantArray` you can use the new version 9 `ARMAProcess` to replace the `ARMAList` in the notebook.
You can try package I have written for estimating garch process parameters -although it's not finished yet but you can estimate around 10 kinds of garch processes.Just type Ugarch in documentation when you install the package.Any feedback is more than welcome.

<https://www.4shared.com/zip/Rb7AXlxYba/garch.html>

These are actually ported R functions package via Rlink.

And here you have example of mathematica code for estimating parameters,this is the fastest code I could write,there are other examples but they are 5-10 times slower...
You will see that the Mathematica optimizer isn't up to task unfortunately so you would have to adjust precision goal for satisfying results...

<https://www.4shared.com/file/rHYRzuB8ba/Garch_estimation_mathematica.html>