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<p>Accurate forecasting of agricultural commodity prices is essential for stabilizing markets and guiding production planning, yet potato price dynamics remain challenging to model due to their pronounced non-stationarity, seasonal variability, and sensitivity to sudden supply and demand disturbances. While recent deep learning models can capture complex temporal dependencies, their training objectives are typically based on point-wise regression losses, which emphasize numerical accuracy but do not preserve the temporal and spectral structure of real market trajectories. As a result, predictions may appear close in magnitude yet misalign in phase, distort local fluctuations, or fail to reproduce nonlinear interactions across temporal scales. To address this issue, we propose a unified causal poly-spectral transport loss that aligns predictions and ground truth in both the time–frequency domain and the higher-order spectral domain. The loss enforces causal optimal transport to maintain the timing of energy distribution across frequencies, while bispectral phase-coupling constraints preserve nonlinear relationships between seasonal and short-term oscillatory patterns. The formulation is fully differentiable, model-agnostic, and compatible with a wide range of forecasting backbones without architectural modification. Experiments on weekly potato price data from 25 provinces in China show consistent improvements across convolutional, recurrent, and transformer-based models, demonstrating that the proposed loss enhances both numerical accuracy and structural fidelity in forecasting real-world agricultural market dynamics.</p>

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Causal Poly-Spectral Transport Loss for Potato Price Forecasting

  • 期刊论文

  • 发表日期：

    2026年3月28日

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  • Zhaoyang Li,
  • Xiaohui Luo

摘要

Accurate forecasting of agricultural commodity prices is essential for stabilizing markets and guiding production planning, yet potato price dynamics remain challenging to model due to their pronounced non-stationarity, seasonal variability, and sensitivity to sudden supply and demand disturbances. While recent deep learning models can capture complex temporal dependencies, their training objectives are typically based on point-wise regression losses, which emphasize numerical accuracy but do not preserve the temporal and spectral structure of real market trajectories. As a result, predictions may appear close in magnitude yet misalign in phase, distort local fluctuations, or fail to reproduce nonlinear interactions across temporal scales. To address this issue, we propose a unified causal poly-spectral transport loss that aligns predictions and ground truth in both the time–frequency domain and the higher-order spectral domain. The loss enforces causal optimal transport to maintain the timing of energy distribution across frequencies, while bispectral phase-coupling constraints preserve nonlinear relationships between seasonal and short-term oscillatory patterns. The formulation is fully differentiable, model-agnostic, and compatible with a wide range of forecasting backbones without architectural modification. Experiments on weekly potato price data from 25 provinces in China show consistent improvements across convolutional, recurrent, and transformer-based models, demonstrating that the proposed loss enhances both numerical accuracy and structural fidelity in forecasting real-world agricultural market dynamics.