Minimax estimation for time series models

The minimax principle is very important for all the fields of statistical science. The minimax approach is to choose an estimator which protects against the largest risk possible. In this paper we show that the Whittle estimator becomes a minimax estimator for the prediction error loss. It is shown that the Whittle estimator is a Bayes estimator for Jeffreys’ prior. Because the minimax approach is very immature in time series analysis, the result shows another advantage of the Whittle estimator.