Hugo Moreira presents a critical examination of the Granularity Paradox in time-series forecasting in a paper submitted on July 5, 2026. This phenomenon reveals how finer temporal disaggregation, such as transitioning from monthly to weekly or daily data, enhances in-sample diagnostics while simultaneously degrading out-of-sample accuracy due to recursive error compounding.
Understanding Temporal Disaggregation
The paper elaborates on the trade-offs involved in temporal data aggregation. While finer granularity increases the dataset size (N) and improves in-sample diagnostics, it introduces significant risks of compounding errors over extended forecasting horizons (H). In contrast, coarser aggregation, such as annual data, mitigates recursive error propagation but limits the data available for estimators.
Moreira benchmarks ten forecasting models, which range from naïve and statistical to machine learning and deep learning architectures, across six different granularities using a comprehensive 13-year public procurement dataset. The findings indicate a non-monotonic threshold structure; for instance, recursive autoregressive models perform poorly under high-frequency forecasting.
Model Performance Across Different Granularities
Empirical results from the study reveal that models like Holt-Winters exhibit substantial degradation, achieving a Test R-squared of -151 and a Total Percentage of Forecast Error (TPFE) of 425.85% at the daily granularity. Conversely, the LSTM model shows a U-shaped error curve, initially worsening from a TPFE of 19.66% at monthly granularity to 35.94% at bi-weekly before improving to a TPFE of 4.35% and an R-squared of 0.66 at daily granularity.
Interestingly, traditional models such as Linear Regression remain stable across all granularities, with a TPFE ranging from 16.3% to 17.0%. This stability suggests that the paradox is primarily driven by the recursive feedback topology rather than the complexity of the model itself.
Evaluating Forecast Accuracy
Moreira emphasizes that standard pointwise metrics, such as RMSE and MAE, often obscure cumulative error propagation. Evaluating forecasts without considering goal-dependent cumulative metrics can lead to misleading assessments of model adequacy. The paper introduces a consensus-dissensus diagnostic tool that compares the directional behavior of pointwise metrics against cumulative TPFE across different granularities, thereby facilitating the identification of models whose diagnostics might mask systematic error propagation.
- Key Findings:
- Granularity affects forecasting accuracy significantly.
- Higher frequency data can lead to recursive error compounding.
- Models exhibit varying performance based on data granularity.
🤖 This article was rewritten by Feed and Figures' editorial AI from a report originally published by arXiv Machine Learning. Facts and quotes are preserved from the original; the rewrite focuses on clarity and structure. For the unedited original, see the source link below.
