Regression coefficient(s) when explanatory & response variables are time series
You should also have a look at the Cross Validated forum on StackExchange a lot questions asked there are related to time series analysis. 

What you are looking for seems like a "Dynamic Regression or "Intervention Analysis" https://www.otexts.org/fpp/9/1 (with examples in R)

An here https://onlinecourses.science.psu.edu/stat510/node/72 you will find a procedure which does an ordinary linear regression but investigates the autocorrelated errors caused by the time series structure of your data (also with an example in R)