# build and estimate a time series process

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..

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I forgot to say that "eta(t)" are iid from N(0,1) –  user6952 Apr 16 '13 at 20:09
–  PlatoManiac Apr 16 '13 at 23:13
To be fair, that notebook on Verbeia.com is very old - probably version 4 vintage. @PlatoManiac - how come you remember what is on my web site better than I do? –  Verbeia Apr 17 '13 at 6:36
@Verbeia Not my ordinary neural net but all credit goes to proper keyword search in Google! However if you change AppendRows[a,b] with Join[a,b,2] and ZeorMatrix using ConstantArray you will be left with properly using the new version 9 ARMAProcess to replace your ARMAList. Then we can have a nice post here from you. Looking forward to it! –  PlatoManiac Apr 17 '13 at 7:19
@PlatoManiac I'll try to get to it tonight. –  Verbeia Apr 17 '13 at 8:02

You could try Verbeia's notebook, 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.

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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

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