Universal data compression and linear prediction

The relationship between prediction and data compression can be extended to universal prediction schemes and universal data compression. Previous work shows that minimizing the sequential squared prediction error for individual sequences can be achieved using the same strategies which minimize the sequential code length for data compression of individual sequences. Defining a "probability" as an exponential function of sequential loss, results from universal data compression can be used to develop universal linear prediction algorithms. Specifically, we present an algorithm for linear prediction of individual sequences which is twice-universal, over parameters and model orders.