Convergence rates for density estimators of weakly dependent time series

Assuming that (Xn)n∈Z is a vector valued time series with a common mar-ginal distribution admitting a density f, our aim is to provide a wide range of consistent estimators of f. We consider different methods of estimation as kernel, projection or wavelets ones. Various cases of weakly dependent series are investigated including the Doukhan & Louhichi’s η-weak dependence con-dition (see [DL99]) and the φ̃-dependence of Dedecker & Prieur (see [DP04]). We thus obtain results for Markov chains, dynamical systems, bilinear mod-els, non causal Moving Average... ¿From a moment inequality of Doukhan & Louhichi, we provide convergence rates of the term of Lq-error or for the uniform bounds on compact sets, in mean or almost surely.