  In this article 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.
