  Accretion disc turbulence along with its effect on large-scale magnetic
fields plays an important role in understanding disc evolution in general, and
the launching of astrophysical jets in particular. Motivated by enabling a
comprehensive sub-grid description for global long-term simulations of
accretions discs, we aim to further characterize the transport coefficients
emerging in local simulations of magnetorotational disc turbulence. For the
current investigation, we leverage a time-dependent version of the test-field
method, which is sensitive to the turbulent electromotive force (EMF) generated
as a response to a set of pulsating background fields. We obtain Fourier
spectra of the transport coefficients as a function of oscillation frequency.
These are well approximated by a simple response function, describing a
finite-time build-up of the EMF as a result of a time-variable mean magnetic
field. For intermediate timescales (i.e., slightly above the orbital
frequency), we observe a significant phase lag of the EMF compared to the
causing field. Augmented with our previous result on a non-local closure
relation in space, and incorporated into a suitable mean-field description that
we briefly sketch out here, the new framework will allow to drop the
restrictive assumption of scale separation.
