We provide a complete description of the set of all solutions to an autoregressive law of motion in a finite-dimensional complex vector space. Every solution is shown to be the sum of three parts, each corresponding to a directed flow of time. One part flows forward from the arbitrarily distant past
one flows backward from the arbitrarily distant future
and one flows outward from time zero. The three parts are obtained by applying three complementary spectral projections to the solution, these corresponding to a separation of the eigenvalues of the autoregressive operator according to whether they are inside, outside or on the unit circle. We provide a finite-dimensional parametrization of the set of all solutions.