This paper:
Measuring Information Transfer
introduced the transfer entropy, a measure which is able to distinguish driving and responding elements and to detect asymmetry in the coupling of subsystems. It consider two systems that may be approximated by stationary Markov processes of order $k$ and $l$ respectively. In the paper I read that the most natural choices is $l = k$. Why? Intuitevely, I think that Markov order/number of lags should be identical for both time series to facilitate interpretation of results.
Can someone give me a more precise answer to this question?