That's the problem and benefit of indices. People use them to reduce factors to a common scale (which lops-off peaks and valleys) and also to remove or reduce or filter stochasticity which also reduces periodicity. So you end-up with smoothed functional relationships. And then we compare smoothed relationships, conveniently ignoring all of the "noise". But we know that probably hidden among the noises things that it would be nice to know, like cyclical functions.

My favorite trick (or stupid focking move, depending on one's perspective) is to plot data on log-log paper. Low and behold a linear relationship is revealed!