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.

翻译：高维时间序列的预测是一项具有挑战性的任务,因为存在着维度问题的诅咒。ARIMA或VAR等古典参数模型需要强有力的模型假设和时间固定性,而且往往过于平衡。本文件利用最近多方面学习的想法提出了一种新的灵活办法。考虑的模型包括线性模型,如中央子空间模型和ARIMA作为特定案例。拟议的程序将多种分解技术和简单的非参数预测结合起来,按当地平均计算。由此产生的程序表明实际生活生态计量时间序列的非常合理性能。我们还为多重估计程序提供了理论上的理由。