  Prediction for high dimensional time series is a challenging task due to the
curse of dimensionality problem. Classical parametric models like ARIMA or VAR
require strong modeling assumptions and time stationarity and are often
overparametrized. This paper offers a new flexible approach using recent ideas
of manifold learning. The considered model includes linear models such as the
central subspace model and ARIMA as particular cases. The proposed procedure
combines manifold denoising techniques with a simple nonparametric prediction
by local averaging. The resulting procedure demonstrates a very reasonable
performance for real-life econometric time series. We also provide a
theoretical justification of the manifold estimation procedure.
