Consider a strictly stationary time series Z_t taking values in R^q . Let Z_1,\ldots, Z_n+k be consecutive observations of Z_t , where k , n are positive integers. Assume the existence of a function r satisfying r(z_1,\ldots, z_k) = E(\varphi (Z_k+1)\mid (Z_1,\ldots, Z_k) = (z_1,\ldots, z_k)) , where \varphi is a continuous real-valued function which is not necessarily bounded. The main problem under consideration is that of nonparametrically estimating r(z_1,\ldots, z_k) .

Kernel types estimates of marginal densities and of the function r are investigated. Under general conditions, strong consistency of the estimates are established. The estimates can be chosen to achieve the optimal rate of convergence (n^-1 \log \,n)^1/(2+d) in L_\infty norm restricted to compact sets. The series Z_t is assumed to satisfy a weak dependence condition reminiscent of the absolute regularity condition. The results on the density estimates are employed to construct consistent estimates of the dependence coefficients and their rates of decay.