I like @RM 's approach. Another one, with a more "mathematical" notation (but I must say I'm not certain of the random behaviour of the way I'm getting the numbers) could be the following

First we create the discrete noise

```
i : noise["Seed"] := i = RandomInteger[{-# , #}] &[Developer`$MaxMachineInteger];
noise[n_Integer] :=
BlockRandom[SeedRandom[# + n];
RandomVariate[NormalDistribution[]]] &[noise["Seed"]]
```

Now, `noise`

is a realisation of the process. You can realise another one by resetting the seed with `noise["Seed"]=.;`

If you do `DiscretePlot[noise[n], {n, 0, 10}]`

several times, you'll see what I mean.

Now, just use `RecurrenceTable`

```
RecurrenceTable[{
x[0] == 0.5,
x[1] == 0.54,
x[2] == -2.3,
x[n] == noise[n] + 0.75 x[n - 1] - 0.23 x[n - 2] + 0.2 x[n - 3]},
x[n], {n, 0, 10}]
```

I think something like my answer here is what you want. This is the same (or nearly the same) as that question, but yours is much clearer. I guess I'll hold off on voting to close...

– rm -rf – 2012-05-17T01:09:49.9201All the answers were good. I learned something from you all; I'm glad I asked. Yes, I meant "generate" when I said "find". – Emre – 2012-05-17T05:20:15.653