Analyzing time series association I am pretty new for time series analysis and I would like to share one of my research questions.

Here is the graph:


Apparently, both 1 and 2 are time series data. 1 represents monthly humidity and 2 represents a morbidity rate. 

I would like to analyze if the morbidity rate (2) is associated with seasonal humidity (1), what method is the best in this scenario? Also, from the visualization, it seems like the morbidity peak is about 3 months after the peak of humidity. 

Can anyone give me some suggestions of this question?

Thank you for any replies!
Here's some ways what I would try:


Shift humidity for n days, which makes Pearson correlation coefficient minimize.
Extract frequencies using Fourier Transform etc.
Do power spectral density estimation using Welch's method etc.