🤖 AI Summary
This study addresses the “granularity paradox” in time series forecasting, wherein fine-grained modeling improves in-sample fit but suffers from error accumulation due to recursive structures, degrading out-of-sample performance, while coarse-grained approaches incur information loss. Leveraging 13 years of public procurement data, the authors systematically evaluate ten model classes—spanning statistical, machine learning, and deep learning methods—across six temporal granularities using multidimensional metrics including TPFE, R², and RMSE. Their analysis reveals that recursive feedback topology, rather than model complexity, is the primary driver of error propagation. The work introduces a “consensus–discrepancy diagnostic” framework and advocates incorporating cumulative error metrics to overcome limitations of conventional point-wise error measures. Empirical results demonstrate strong model-dependent granularity effects—for instance, LSTM achieves a TPFE of 4.35% at daily granularity, whereas Holt-Winters fails catastrophically with R² = −151.
📝 Abstract
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.