# 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..

• I forgot to say that "eta(t)" are iid from N(0,1) – Moez K 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.