How to statistically compare the trend similarity of two distinct time series?


No cake for spunky
"As a biologist, I thought that the trend comparison between two distinct time series would be fairly simple. "

I used to think this too, before I started reading time series a decade ago. :p Simple time series does not exist. Well accurate simple time series does not.

I am not a biologist and I have no idea what is common in that field in this area. My bet is that time series is not used regularly in that profession. It is common to some extent in economics, policy, physics, finance and in some form education. But each prefers different approaches.