Twice universal linear prediction of individual sequences

We present a “twice universal” linear prediction algorithm over the unknown parameters and model orders, in which the sequentially accumulated square prediction error is as good as any linear predictor of order up to some M, for any individual sequence. The extra loss comprises of a parameter “redundancy” term proportional to (p/2)n^-1ln(n), and a model order “redundancy” term proportional to n^-1ln(p), where p, is the model order we compare with, and n is the data length. The computational complexity of the algorithm is about the complexity of a recursive least squares (RLS) linear predictor of order M