I am trying to compare two data sets available for x number of historical months. These are two different types of claims, i.e. first party claims and third party claims. We know that third party claims will increase if first party claims increase and vice versa, after a lag of few months.

How can I know the lag in monhts between the two type of claims. We recently experienced increase in first party claims. So now we want to estimate the number of months after which we will see a corresponding increase in third party claims.

There is strong monthly seasonality factor that is creating complications.

Thank you for your help.