Strongly Consistent Nonparametric Forecasting and Regression for Stationary Ergodic Sequences

摘要

Let {(X_i, Y_i)} be a stationary ergodic time series with (X, Y) values in the product space R~d direct X 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.