I have read blogs posts that say one should use monthly, quarterly or annual data depending on whether you want to predict monthly, quarterly or annual outcome respectively.
So I guess the same applies to studying the dynamics of two or more variables using a VAR model. For example, the response of $y_t$ to a shock in $x_t$ should be expected to be different at monthly, quarterly and annual frequencies, right? It appears so in my experiment in the attached figure.
So saying that "the response of $y_t$ to a shock in $x_t$ is positive" is incomplete, I guess. Perhaps, it is better to say, "the response of $y_t$ to a shock in $x_t$ is positive at annual frequency, negative at quarterly frequency, and so on".
Or it is that the results should be similar irrespective of the frequency of the data?