  We study the problem of parameter estimation in time series stemming from
general stochastic processes, where the outcomes may exhibit arbitrary temporal
correlations. In particular, we address the question of how much Fisher
information is lost if the stochastic process is compressed into a single
histogram, known as the empirical distribution. As we show, the answer is
non-trivial due to the correlations between outcomes. We derive practical
formulas for the resulting Fisher information for various scenarios, from
generic stationary processes to discrete-time Markov chains to continuous-time
classical master equations. The results are illustrated with several examples.
