越细的时间粒度，模型在训练时表现越好，但预测误差越大，这是因误差累积导致的。
The Granularity Paradox: How Temporal Disaggregation Inflates In-Sample Fit and Compounds Out-of-Sample Error
- 细粒度时间数据虽提升样本拟合，却因误差递推而降低外推精度。
- 日度预测下，LSTM误差先升后降，而传统模型如霍尔特-温特斯错误率飙升至425.85%。
- 标准误差指标会掩盖累计误差，需用方向一致性诊断识别隐藏问题。
本文探讨时间序列预测中的「粒度悖论」：更细的时间粒度（如月度→周度/日度）虽改善样本内拟合与数据量（N），但因递推误差在更长预测跨度（H）中累积，导致外样本准确率下降。相反，粗粒度聚合（如年度）虽消除误差传播，却减少可用数据。研究通过13年公共采购数据，对10种模型（涵盖朴素、统计、机器学习与深度学习）在六种粒度上进行基准测试。结果呈现非单调阈值结构：递归自回归与季节性模型在高频预测下显著恶化（如霍尔特-温特斯日度预测测试R²为-151，TPFE达425.85%）；而LSTM呈U形误差曲线，从月度（19.66% TPFE）升至双周（35.94%）后，在日度时逆转至TPFE 4.35%、R² 0.66。线性回归在所有粒度上稳定（TPFE 16.3–17.0%），证明该悖论源于递推结构而非模型复杂度。结果表明，标准点对点指标（如RMSE、MAE）系统性掩盖累计误差传播，缺乏目标依赖的累积指标会导致模型评估失真。研究提出共识-分歧诊断法，通过比较点对点指标与累积TPFE在不同粒度下的方向一致性，识别出被常规指标掩盖系统误差传播的模型。
原文摘要 · Abstract (English)
This paper explores the "Granularity Paradox" in time-series forecasting, wherein finer temporal disaggregation (e.g., Monthly to Weekly/Daily) improves in-sample diagnostics and dataset size (N), but degrades out-of-sample accuracy due to recursive error compounding over longer horizons (H). Conversely, coarse aggregation (Annual) eliminates recursive error propagation but reduces data available to estimators. We formalize this trade-off and benchmark 10 models - spanning naïve, statistical, machine learning, and deep learning architectures - across six granularities using a 13-year public procurement dataset. The empirical results reveal a non-monotonic threshold structure: recursive autoregressive and seasonal models degrade substantially under high-frequency forecasting (e.g., Holt-Winters reaches a Test R-squared of -151 and TPFE of 425.85% at the Daily grain), while the LSTM traces a U-shaped error curve, worsening from Monthly (19.66%) through Bi-Weekly (35.94%) before overcoming the error propagation penalty at Daily (TPFE of 4.35%, R-squared of 0.66). Linear Regression remains stable across all granularities (16.3-17.0% TPFE), confirming that the paradox is driven by recursive feedback topology, not model complexity. The results demonstrate that standard pointwise metrics (RMSE, MAE) systematically mask cumulative error propagation, and that evaluating forecasts without goal-dependent cumulative metrics produces misleading assessments of model adequacy. We introduce a consensus-dissensus diagnostic comparing the directional behaviour of pointwise metrics against cumulative TPFE across granularities, enabling the identification of models whose standard diagnostics mask systematic error propagation.
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