How to choose the lag between the predicated and explanatory variables Building on the question I asked here. If I wanted to determine which forward lag between oil price and number of cars bought best reflects a strong relationship, does it make sense to just compare the adjust R^2 associated with lags from say 1 to 20 and choose the one with the highest one or could there be a better way, as this is currently what I have done? 
Thanks
 A: Run the cross correlation analysis. It's similar to autocorrelation function (ACF). You apply different lags from negative to positive to calculate the covariance between series while scaling the values by contemporaneous covariance. Cross correlation may give you an idea about the lags. 
Another consideration is the autocorrelation in the series. If both series are heavily autocorrelated then the results of cross correlation will not be reliable. I wouldn't be surprised is the number of cars sold was an extremely persistent series. Oil price is certainly persistent. Therefore, you may want to apply differencing to the series before running cross correlation analysis.
Though you must be careful not to make causal inferences that are based solely on this kind of analysis. I could easily argue that the number of cars bought should impact the demand for oil, and oil prices as a result. It is also conceivable that instead of depressing the number of cars sold increasing oil prices may shift the demand towards smaller cars or push the miles driven down. It is also possible that the relationship goes both ways (simultaneous), that oil prices influence cars sold, and cars sold influence oil prices. In other words, you may have an endogeneity problem at hand.
