  In this paper, we obtain generic bounds on the variances of estimation and
prediction errors in time series analysis via an information-theoretic
approach. It is seen in general that the error bounds are determined by the
conditional entropy of the data point to be estimated or predicted given the
side information or past observations. Additionally, we discover that in order
to achieve the prediction error bounds asymptotically, the necessary and
sufficient condition is that the "innovation" is asymptotically white Gaussian.
When restricted to Gaussian processes and 1-step prediction, our bounds are
shown to reduce to the Kolmogorov-Szeg\"o formula and Wiener-Masani formula
known from linear prediction theory.
