论文标题
基于歧管的时间序列预测
Manifold-based time series forecasting
论文作者
论文摘要
由于维度问题的诅咒，高维时间序列的预测是一项具有挑战性的任务。经典的参数模型（例如Arima或var）需要强大的建模假设和时间平稳性，并且经常被过多兼容。本文使用最新的多种学习思想提供了一种新的灵活方法。考虑的模型包括线性模型，例如中央子空间模型和Arima，作为特定情况。所提出的程序将歧管授予技术与通过局部平均的简单非参数预测相结合。最终的过程表明了现实生活中的计量经济学时间序列非常合理的表现。我们还提供了多种估计程序的理论理由。
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.
