They probably mean that an IV is influencing the DV at different points in time. So X may have one impact on Y at t and a second impact at t+1. But it is also possible they mean the DV itself is influencing itself at latter points in time. So Yt predicts Yt+1. You can not use linear regression to model the latter (you need something like autoregressive distributed lag ARDL) and unlike normal AR regression if you have lags of Y in your model and get the AR error wrong it will bias your results not just mess up the statistical test.

I am not certain from the symbols what they are doing here, they are different than what I have seen for time series.