How to get a robust cross correlation relationship between variables.
Question to all of the quants here:
Say I have a time series variable X that is statistically significant with Y. However, when plotting the cross correlation function between lags of X and Y, one of the lags (say lag 3) of X is shown to have a higher correlation with Y than all other lags of X (including lag0). How would I statistically show that the lag relationships exists/is robust and not just because of noise? The data source is monthly data 20+ years. I did try to smooth out the data with PCA and the lag relationship still exists. I just don’t have any fundamental basis to explain why it exists.
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