We consider the problem of $L_p$-consistent density estimation from the initial segments of strongly dependent processes. It is shown that no procedure can consistently estimate the one-dimensional marginal density of every stationary ergodic process for which such a density exists. A similar result is established for the problem of estimating the support of the marginal distribution of an ergodic process.
"On density estimation from ergodic processes." Ann. Probab. 26 (2) 794 - 804, April 1998. https://doi.org/10.1214/aop/1022855650