Prediction and MDL for infinite sequences

We combine Solomonoff's approach to universal prediction with algorithmic statistics and suggest to use the computable measure that provides the best "explanation" for the observed data (in the sense of algorithmic statistics) for prediction. In this way we keep the expected sum of squares of prediction errors bounded (as it was for the Solomonoff's predictor) and, moreover, guarantee that the sum of squares of prediction errors is bounded along any Martin-Löf random sequence. An extended abstract of this paper was presented at the 16th International Computer Science Symposium in Russia (CSR 2021) (Milovanov 2021).