  We derive finite time error bounds for estimating general linear
time-invariant (LTI) systems from a single observed trajectory using the method
of least squares. We provide the first analysis of the general case when
eigenvalues of the LTI system are arbitrarily distributed in three regimes:
stable, marginally stable, and explosive. Our analysis yields sharp upper
bounds for each of these cases separately. We observe that although the
underlying process behaves quite differently in each of these three regimes,
the systematic analysis of a self--normalized martingale difference term helps
bound identification error up to logarithmic factors of the lower bound. On the
other hand, we demonstrate that the least squares solution may be statistically
inconsistent under certain conditions even when the signal-to-noise ratio is
high.
