The Granularity Paradox: How Temporal Disaggregation Inflates In-Sample Fit and Compounds Out-of-Sample Error
This paper explores the 'Granularity Paradox' in time-series forecasting, where finer temporal disaggregation improves in-sample diagnostics but degrades out-of-sample accuracy due to recursive error compounding over longer horizons. Benchmarking 10 models across six granularities on a 13-year procurement dataset reveals a non-monotonic threshold: recursive models (e.g., Holt-Winters) degrade severely at high frequencies, LSTM exhibits a U-shaped error curve, and linear regression remains stable. Standard pointwise metrics mask cumulative error; a consensus-dissensus diagnostic is introduced.
-->
[Submitted on 5 Jul 2026]
Title:The Granularity Paradox: How Temporal Disaggregation Inflates In-Sample Fit and Compounds Out-of-Sample Error
View a PDF of the paper titled The Granularity Paradox: How Temporal Disaggregation Inflates In-Sample Fit and Compounds Out-of-Sample Error, by Hugo Moreira
View PDF HTML (experimental)
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.
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Methodology (stat.ME)
MSC classes: 62M10, 62P20, 68T07
ACM classes: G.3; I.2.6
Cite as: arXiv:2607.05450 [cs.LG]
(or arXiv:2607.05450v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.05450
arXiv-issued DOI via DataCite
Submission history
From: Hugo Moreira [view email] [v1] Sun, 5 Jul 2026 11:52:08 UTC (44 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled The Granularity Paradox: How Temporal Disaggregation Inflates In-Sample Fit and Compounds Out-of-Sample Error, by Hugo Moreira
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.LG
new | recent | 2026-07
Change to browse by:
cs cs.AI stat stat.ME
References & Citations
NASA ADS
Google Scholar
Semantic Scholar
Loading...
Data provided by:
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data, Media
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Related Papers
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
IArxiv recommender toggle
IArxiv Recommender (What is IArxiv?)
Author
Venue
Institution
Topic
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)