I'm trying to figure out how to model two time series where there is zero correlation on the short term but we suspect that there is a long term correlation. I'm not even sure if this is possible from definition...We are looking at the inflation rate between US and Aus, and on short term (month to month points) the correlation is pretty much zero. But from a fundamental view, we suspect that in the long term they are correlated. How would I go about dis/proving this hypothesis?And if it turns out that they are correlated in the long term, how would I model these two time series? Modelling correlated time series is trivial, but with different short/long term coefficients?thanks.

I think this is normal that such time series appear decorrelated when you look at shorter terms. For example, you expect IBM and DELL to be quite correlated in the long term, but not really in a one day period since it can depend on special announcements for one firm for example. I think that if you simulate correlated series, they will be more correlated in the long term than in a short term, so you shouldnt have to do anything special for this.

QuoteOriginally posted by: OzQuantI'm trying to figure out how to model two time series where there is zero correlation on the short term but we suspect that there is a long term correlation. I'm not even sure if this is possible from definition...We are looking at the inflation rate between US and Aus, and on short term (month to month points) the correlation is pretty much zero. But from a fundamental view, we suspect that in the long term they are correlated. How would I go about dis/proving this hypothesis?And if it turns out that they are correlated in the long term, how would I model these two time series? Modelling correlated time series is trivial, but with different short/long term coefficients?thanks.Try looking up "cointegration", there is an FAQ thread on it...

A non-zero long-term correlation is possible with a short-term zero correlation; but the time series cannot be independent over all short intervals but depedent over long ones. Also, as sleger says, it is both possible and common to have short-term correlations that are obscured by noise while long-term correlations stand out.But, as exotiq points out, this is not your problem. You find that short-term changes in inflation rates are close to uncorrelated, but believe in theory that long-term levels should move together (presumably because you think that long-term inflation is determined by global economic parameters rather than national economic and monetary policies). The short-term part is easy to test with standard statistics, the long-term one is close to untestable. Once you start testing over intervals on the order of a decade, you are betrayed by the definitional and measurement problems with inflation, the small number of non-overlapping data intervals and the difficulty of adjusting for regime changes.The only hope I see would be to test if expectations of long-term inflation are correlated. You can derive these from security prices, and test over short intervals (you're testing short-term changes in long-term expectation; which might or might not address your questions of interest).

Just FYI, you can also use PCA for this, and you could show the same results as for the interest rates, meaning you will get the same three factors explaining the moves in your curve. If you need further precised explanation on this, please ask me.

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