Hi,

it really depends on what you are trying to prove/check. If you use data in levels, you are reporting if your variables are evolving on the same/similar trend but if you use 1st order diff transformation, you report info on their joint dynamics - which is probably what you need. 

Also if I remember correctly, as the cross-corelation is basically normalized function of cross-covariance, your variables should be at least weakly stationary (without the necessary math, I just say that while stationarity is not a condition, stationary sample correlation tends to true correlation). Again, this would serve in favor of using diff transformation.

Hope this helps a little

Martin

PS. While looking at your example, you probably would not get much far with just cross-correlation analysis as there should be cleary some time-dependence (and lag) between your variables of interest so I would recommend to use some basic regression function the least (preferably with panel data structure to check your hypothesis at wider sample). 

Dear Martin

Thanks a lot.

Hi Sun,

Martin has got nearly everything you might need. I am just adding some names of the test that you may want to try. To test the initial correlation between the two variables, you can use a Johansen Cointegration test. The test can also be performed on the diff'ed data if you want to test the correlation of the "increase" of the two variables. Also, you can try Granger Causality test if you want to detect the lagged effect between the two variables. Lastly, you can use ECM as a adjusted method of testing cointegration, since it allows both the inclusion of other variables and the inclusion of an adjustment for lagged "unbalance". (But do make sure you check for cointegration first before you use ECM.)

Hope it helps,

Joy