  We consider a finite impulse response system with centered independent
sub-Gaussian design covariates and noise components that are not necessarily
identically distributed. We derive non-asymptotic near-optimal estimation and
prediction bounds for the least-squares estimator of the parameters. Our
results are based on two concentration inequalities on the norm of sums of
dependent covariate vectors and on the singular values of their covariance
operator that are of independent value on their own and where the dependence
arises from the time shift structure of the time series. These results
generalize the known bounds for the independent case.
