Manifold-based time series forecasting

TL;DR

This paper introduces a manifold learning-based approach for high-dimensional time series forecasting, combining denoising and nonparametric prediction, which outperforms classical models in econometric applications.

Contribution

It proposes a novel manifold-based method that generalizes linear models like ARIMA, with theoretical justification and practical effectiveness demonstrated on real data.

Findings

Effective forecasting of high-dimensional econometric time series

The method outperforms classical parametric models in experiments

Theoretical analysis supports the manifold estimation approach

Abstract

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.