On universal linear prediction of Gaussian data

In this paper, we derive some of the stochastic properties of a universal linear predictor, through analyses similar to those generally made in the adaptive signal processing literature. In [1], a predictor was introduced whose sequentially accumulated mean squared error for any bounded individual sequence was shown to be as small as that for any linear predictor of order less than some maximum order m. For stationary Gaussian time series, we generalize these results, and remove the boundedness restiriction. In this paper we show that the learning curve of this universal linear predictor is dominated by the learning curve of the best order predictor used in the algorithm.