Shrinkage Estimation and Prediction for Time Series

For independent samples, shrinkage estimation theory has been developed systematically. Although shrinkage estimators are biased, they improve the MSE of unbiased ones. In view of this, we will develop shrinkage estimation theory and prediction for dependent samples. First, we propose a shrinkage estimator for the coefficients of AR model, which improves the MSE of the least squares estimator. Second, we discuss the problem of shrinkage prediction , and propose a shrinkage predictor which improves the prediction error of the best linear predictor with finite lag length. The results are applied to portfolio estimation etc. We provide numerical studies, which show some interesting features of shrinkage problems in time series analysis.