Rethinking Channel Dependence for Multivariate Time Series Forecasting: Learning from Leading Indicators

TL;DR

This work investigates leveraging locally stationary lead-lag relations between variates to enhance multivariate time series forecasting. It introduces LIFT, a plug-and-play framework that first estimates leading indicators and their lead steps via cross-correlation $R^{(j)}_{i,t}(δ)$ and then refines lagged variates with target-oriented shifts and an Adaptive Frequency Mixer. A lightweight variant, LightMTS, demonstrates parameter efficiency comparable to linear baselines. Across six real-world datasets, LIFT consistently improves both CI and CD backbones, validating the practicality of learning from leading indicators.

Abstract

Recently, channel-independent methods have achieved state-of-the-art performance in multivariate time series (MTS) forecasting. Despite reducing overfitting risks, these methods miss potential opportunities in utilizing channel dependence for accurate predictions. We argue that there exist locally stationary lead-lag relationships between variates, i.e., some lagged variates may follow the leading indicators within a short time period. Exploiting such channel dependence is beneficial since leading indicators offer advance information that can be used to reduce the forecasting difficulty of the lagged variates. In this paper, we propose a new method named LIFT that first efficiently estimates leading indicators and their leading steps at each time step and then judiciously allows the lagged variates to utilize the advance information from leading indicators. LIFT plays as a plugin that can be seamlessly collaborated with arbitrary time series forecasting methods. Extensive experiments on six real-world datasets demonstrate that LIFT improves the state-of-the-art methods by 5.5% in average forecasting performance. Our code is available at https://github.com/SJTU-Quant/LIFT.

Figures (8)

• Figure 1: Illustration of locally stationary lead-lag relationships. (a) On training data, three variates $v_1$, $v_2$, and $v_3$ share similar temporal patterns (see colors) across the lookback window and horizon window, while $v_1$ and $v_2$ run ahead of $v_3$ by four and two steps, respectively. However, the leading indicators and leading steps can only keep static for a short period. (b) On test data, $v_1$ is no longer a leading indicator, and $v_2$ also changes its leading steps to five.
• Figure 2: Illustration of our key idea. In one case of test data, $v_1$ no longer leads $v_3$. Instead, the leading indicators of $v_3$ are $v_2$ and $v_4$, which lead by five and three steps, respectively. An intuitive idea is to shift $v_2$ and $v_4$ by the corresponding leading steps to keep them always aligned with $v_3$.
• Figure 3: Overview of LIFT. All layers in the grey background are non-parametric. We depict the input of the lookback window by solid curves and the predictions of the horizon window by dashed curves. As an illustration, we choose the two most possible leading indicators for each target variate, e.g., the orange and the yellow ones are leading indicators of the red at time $t$.
• Figure 4: Architecture of the adaptive frequency mixer.
• Figure 5: (a) Performance comparison between LightMTS and all baselines; (b) Performance comparison between variants of LightMTS; (c) Performance of DLinear+LIFT under different numbers of the selected leading indicators (i.e., $K$) and the states (i.e., $N$).

Theorems & Definitions (1)

• Definition 1: Cross-correlation coefficient