  We address the problem of nonparametric estimation of characteristics for
stationary and ergodic time series. We consider finite-alphabet time series and
real-valued ones and the following four problems: i) estimation of the
(limiting) probability (or estimation of the density for real-valued time
series), ii) on-line prediction, iii) regression and iv) classification (or
so-called problems with side information). We show that so-called archivers (or
data compressors) can be used as a tool for solving these problems. In
particular, firstly, it is proven that any so-called universal code (or
universal data compressor) can be used as a basis for constructing
asymptotically optimal methods for the above problems. (By definition, a
universal code can "compress" any sequence generated by a stationary and
ergodic source asymptotically till the Shannon entropy of the source.) And,
secondly, we show experimentally that estimates, which are based on practically
used methods of data compression, have a reasonable precision.
