Quadratic Direct Forecast for Training Multi-Step Time-Series Forecast Models

TL;DR

This paper introduces a quadratic-form weighted training objective for multi-step time-series forecasting, which accounts for label autocorrelation and heterogeneous task importance, leading to improved forecasting accuracy.

Contribution

The paper proposes a novel quadratic-form weighted training objective and a Quadratic Direct Forecast (QDF) algorithm that adaptively updates the weighting matrix for better multi-step forecasting.

Findings

QDF improves forecasting accuracy across various models.

The quadratic weighting captures label autocorrelation effectively.

State-of-the-art results achieved on benchmark datasets.

Abstract

The design of training objective is central to training time-series forecasting models. Existing training objectives such as mean squared error mostly treat each future step as an independent, equally weighted task, which we found leading to the following two issues: (1) overlook the label autocorrelation effect among future steps, leading to biased training objective; (2) fail to set heterogeneous task weights for different forecasting tasks corresponding to varying future steps, limiting the forecasting performance. To fill this gap, we propose a novel quadratic-form weighted training objective, addressing both of the issues simultaneously. Specifically, the off-diagonal elements of the weighting matrix account for the label autocorrelation effect, whereas the non-uniform diagonals are expected to match the most preferable weights of the forecasting tasks with varying future steps. To achieve this, we propose a Quadratic Direct Forecast (QDF) learning algorithm, which trains the forecast model using the adaptively updated quadratic-form weighting matrix. Experiments show that our QDF effectively improves performance of various forecast models, achieving state-of-the-art results. Code is available at https://anonymous.4open.science/r/QDF-8937.