In this work a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary ergodic. N
amely, three problems are considered: goodness-of-fit (or identity) testing, process classification, and the change point problem. For each of the problems a test is constructed that is asymptotically accurate for the case when the data is generated by stationary ergodic processes. The tests are based on empirical estimates of distributional distance.
We propose steganographic systems for the case when covertexts (containers) are generated by a finite-memory source with possibly unknown statistics. The probability distributions of covertexts with and without hidden information are the same; this m
eans that the proposed stegosystems are perfectly secure, i.e. an observer cannot determine whether hidden information is being transmitted. The speed of transmission of hidden information can be made arbitrary close to the theoretical limit - the Shannon entropy of the source of covertexts. An interesting feature of the suggested stegosystems is that they do not require any (secret or public) key. At the same time, we outline some principled computational limitations on steganography. We show that there are such sources of covertexts, that any stegosystem that has linear (in the length of the covertext) speed of transmission of hidden text must have an exponential Kolmogorov complexity. This shows, in particular, that some assumptions on the sources of covertext are necessary.
