  For the past two decades, single-index model, a special case of projection
pursuit regression, has proven to be an efficient way of coping with the high
dimensional problem in nonparametric regression. In this paper, based on weakly
dependent sample, we investigate the single-index prediction (SIP) model which
is robust against deviation from the single-index model. The single-index is
identified by the best approximation to the multivariate prediction function of
the response variable, regardless of whether the prediction function is a
genuine single-index function. A polynomial spline estimator is proposed for
the single-index prediction coefficients, and is shown to be root-n consistent
and asymptotically normal. An iterative optimization routine is used which is
sufficiently fast for the user to analyze large data of high dimension within
seconds. Simulation experiments have provided strong evidence that corroborates
with the asymptotic theory. Application of the proposed procedure to the rive
flow data of Iceland has yielded superior out-of-sample rolling forecasts.
