Consider the grangertest()
in the lmtest library.
It is a test to see if one time series is useful in forecasting another.
A couple references to get you started:
http://monogan.myweb.uga.edu/teaching/ts/index.htmlhttps://spia.uga.edu/faculty_pages/monogan/teaching/ts/
http://monogan.myweb.uga.edu/teaching/ts/Kgranger.pdfhttps://spia.uga.edu/faculty_pages/monogan/teaching/ts/Kgranger.pdf