We address the problem of online prediction for time series. We show that any universal code (or a universal data compressor) can be used as a basis for constructing asymptotically optimal methodsâ€¦ (More)

We suggest a new approach to hypothesis testing for ergodic and stationary processes. In contrast to standard methods, the suggested approach gives a possibility to make tests, based on any losslessâ€¦ (More)

We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) canâ€¦ (More)

The problem of converting a sequence of symbols generated by a Bernoulli source into an unbiased random sequence is well-known in information theory. The proposed method is based on Eliasâ€™ algorithmâ€¦ (More)

We address the problem of constructing an adaptive arithmetic code in the case where the source alphabet is large and there are lots of different symbols with equal counts of occurrence. For anâ€¦ (More)

We show that data compression methods (or universal codes) can be applied for hypotheses testing in a framework of classical mathematical statistics. Namely, we describe tests, which are based onâ€¦ (More)

Kolmogorov complexity furnishes many useful tools for studying different natural processes that can be expressed using sequences of symbols from a finite alphabet (texts), such as genetic texts,â€¦ (More)

The problem of predicting a sequence x1, x2, .... where each xi belongs to a finite alphabet A is considered. Each letter xt+1 is predicted using information on the word x1, x2, ...., xt only. We useâ€¦ (More)