I have two time series and I computed the percentage change like:

(Value at time2)/(Value at time1) - 1

My doubt is on the correlation of the original time series and the percentage change time series.

The correlation for the original time series is -0.2 while for the percentage change is 0.22.

My question is just on a theoretical level: is it possibile to have opposite relationships between the two pairs of time series? How should I interpret this opposite behavior of the two couple of time series?