  Filled skutterudite compound EuFe$_4$As$_{12}$ shows the highest magnetic
ordering temperature of $T_{\rm C}$ = 154 K among Eu-based skutterudite
compounds, but its magnetic ground state has not been determined yet. Here, we
performed $^{153}$Eu nuclear magnetic resonance (NMR) and $^{75}$As nuclear
quadrupole resonance (NQR) measurements on EuFe$_4$As$_{12}$ to reveal its
magnetic ground state as well as the physical properties from a microscopic
point of view. From the temperature and magnetic field dependence of $^{153}$Eu
NMR spectrum in the magnetically ordered state, we found that the Eu ions are
in Eu$^{2+}$ state with a nearly 7 $\mu_{\rm B}$ corresponding to $S$ = 7/2
spins. Combined with the magnetization measurements which show the reduced
saturation moments of 4.5 $\mu_{\rm B}$/f.u., we determined the ground magnetic
structure in EuFe$_4$As$_{12}$ to be ferrimagnetic where the Eu$^{2+}$ 4$f$ and
the Fe 3$d$ ordered moments are ferromagnetically aligned in each sublattice
but the moments between the sublattices are antiferromagnetically aligned. We
also found the local distortion at the Eu site from the cubic symmetry in the
magnetically ordered state. The relationship between the rattling motion of Eu
atoms and the local symmetry of the Eu ions is discussed. From the $^{75}$As
NQR nuclear spin-lattice relaxation time measurements as well as $^{153}$Eu NMR
measurements, we found that the 4$f$ electrons of the Eu ions are well
described by the local moment picture in both the magnetic and paramagnetic
metallic states.
