  Let $\{(X_i,Y_i)\}$ be a stationary ergodic time series with $(X,Y)$ values
in the product space $\R^d\bigotimes \R .$ This study offers what is believed
to be the first strongly consistent (with respect to pointwise, least-squares,
and uniform distance) algorithm for inferring $m(x)=E[Y_0|X_0=x]$ under the
presumption that $m(x)$ is uniformly Lipschitz continuous. Auto-regression, or
forecasting, is an important special case, and as such our work extends the
literature of nonparametric, nonlinear forecasting by circumventing customary
mixing assumptions. The work is motivated by a time series model in stochastic
finance and by perspectives of its contribution to the issues of universal time
series estimation.
