Given a time series $X_1,\dots,X_n,\dots$ taking values in a large (high-dimensional) space $\cX$, we would like to find a function $f$ from $\cX$ to a small (low-dimensional or finite) space $\cY$ such that the time series $f(X_1),\dots,f(X_n),\dots$ retains all the information about the time-series dependence in the original sequence, or as much as possible thereof. This goal is formalized in this work, and it is shown that the target function $f$ can be found as the one that maximizes a certain quantity that can be expressed in terms of entropies of the series $(f(X_i))_{i\in\N}$. This quantity can be estimated empirically, and does not involve estimating the distribution on the original time series $(X_i)_{i\in\N}$.