# Generating data with given Auto and Cross Correlations

I have two discrete vectors $$\mathbf{x}_1$$ and $$\mathbf{x}_2$$, and I'm trying to generate more data $$\mathbf{f}_1$$ and $$\mathbf{f}_2$$ that has some basics properties of $$\mathbf{x}_1$$ and $$\mathbf{x}_2$$. Namely, the same autocorrelations and cross-correlations. It doesn't have to be the exact same, just similar. For example, I can cut the tails off the correlations if that makes it easier.

Is this possible?

• Hi: if the auto-correlations cutoff at some finite lag ( and you were just matching them ) then there's a one to one between the autocorrelations of a series and the ARIMA mapping of that series. So, if you have a series that has say correlations at lag1 and lag2 and zero after that, then you can find the MA(2) that the series maps to. The problem is that you've got a second level that you want to match also which are the cross-correlations. That makes me think that you've got a very difficult problem and I'm not sure how to handle that. – mark leeds Jan 21 at 17:41