  Macroscopic realism, the classical world view that macroscopic objects exist
independently of and are not influenced by measurements, is usually tested
using Leggett-Garg inequalities. Recently, another necessary condition called
no-signaling in time (NSIT) has been proposed as a witness for non-classical
behavior. In this paper, we show that a combination of NSIT conditions is not
only necessary but also sufficient for a macrorealistic description of a
physical system. Any violation of macroscopic realism must therefore be
witnessed by a suitable NSIT condition. Subsequently, we derive an operational
formulation for NSIT in terms of positive operator-valued measurements and the
system Hamiltonian. We argue that this leads to a suitable definition of
"classical" measurements and Hamiltonians, and apply our formalism to some
generic coarse-grained quantum measurements.
