I will give a tutorial lecture for covariance matrix estimation
for time series. Under a short-range dependence condition for a
wide class of nonlinear processes described in Wiener (1958), I
will show that the banded covariance matrix estimates converge in
operator norm to the true covariance matrix with explicit rates of
convergence. Such rates are optimal. I will also consider the
consistency of the estimate of the inverse covariance matrix.
These results are applied to the traditional Wiener-Kolmogorov
prediction theory, and error bounds for the finite predictor
coefficients are obtained.