The differences in spectrum of the DSGE model and the VAR model

Dear Johannes,
Thank you very much for your helpful guidance, I am grateful.
According to the DSGE model in this paper
DSGE1.pdf (726.6 KB)
on page 1723: ‘A consequence of the fact that the model explains just a fraction of the stock market is that our impulse response functions are comparable to those provided by the VAR literature only to a limited extent, given that the VAR assigns to identified structural shocks the description of the whole spectrum of frequencies of the variables in the vector. This motivates, e.g. the moderate response of stock prices to a monetary policy shock, relative to VAR evidence, since what we are capturing is the response to the component that interacts with the rest of the macroeconomy at business cycle frequencies.’
Does this mean that DSGE models focus on business cycle frequencies due to first-order log difference data/HP filtered log data and Kalman filter? whereas the VAR model incorporates all the frequencies/the whole spectrum of the data?
Thank you very much and look forward to hearing from you.
Best regards,

Typically, that is the interpretation we give to the DSGE model. That it models not the whole data movements but rather the cyclical components only. So the model you write down generates artificial data only containing those frequencies. In contrast, the VAR does not easily allow you to separate out particular frequencies (although that would be possible as well). Note that this is not really about the Kalman filter or using other filters. You could also treat the data entering the VAR this way.