Sliced Average Variance Estimation for Multivariate Time Series

TL;DR

This paper introduces TSAVE, a new supervised dimension reduction method for multivariate time series, extending existing techniques like TSIR and proposing a hybrid approach, with evaluations showing their advantages over iid methods.

Contribution

The paper develops TSAVE, a novel time series dimension reduction method, and compares it with TSIR and a hybrid approach, demonstrating their effectiveness for temporal data.

Findings

TSAVE outperforms iid-based methods when using lagged predictors.

Hybrid TSIR-TSAVE combines advantages of both methods.

All proposed methods effectively capture temporal dependencies.

Abstract

Supervised dimension reduction for time series is challenging as there may be temporal dependence between the response $y$ and the predictors $\boldsymbol x$. Recently a time series version of sliced inverse regression, TSIR, was suggested, which applies approximate joint diagonalization of several supervised lagged covariance matrices to consider the temporal nature of the data. In this paper we develop this concept further and propose a time series version of sliced average variance estimation, TSAVE. As both TSIR and TSAVE have their own advantages and disadvantages, we consider furthermore a hybrid version of TSIR and TSAVE. Based on examples and simulations we demonstrate and evaluate the differences between the three methods and show also that they are superior to apply their iid counterparts to when also using lagged values of the explaining variables as predictors.