Shock or innovation in forecast error variance decomposition or historical decomposition

Dear Johannes,
In my DSGE model, all the shocks take autoregressive form, e.g.
Ln(Vt)=Ln(Vbar)+rho*(Ln(Vt-1)-Ln(Vbar))+epsilon,
epsilon ~ N(0,sigma^2)
where Vt is shock, epsilon is the innovation to the shock,
I am wondering which do forecast error variance decomposition and historical decomposition, use, Vt shock or epsilon innovation?
Thank you very much and look forward to hearing from you.
Best regards,
Jesse

It’s always about the innovations \varepsilon_t