The Granularity Paradox: How Temporal Disaggregation Inflates In-Sample Fit and Compounds Out-of-Sample Error
Authors: Hugo Moreira
Organizations: 1CIES - Centro de Investigação e Estudos de Sociologia, Iscte - Instituto Universitário de Lisboa, Lisbon, Portugal.
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.
Modern deep-learning models have achieved remarkable success in time-series forecasting. Yet, their performance degrades in long-term prediction due to error accumulation in autoregressive inference, where predictions are recursively used as inputs. While classical error correction mechanisms (ECMs) have long been used in statistical methods, their applicability to deep learning models remains limited or ineffective. In this work, we revisit the error accumulation problem in deep time-series forecasting and investigate the role and necessity of ECMs in this new context. We propose a simple, architecture-agnostic error correction model that can be integrated with any existing forecaster without requiring retraining. By explicitly decomposing predictions into trend and seasonal components and training the corrector to adjust each separately, we introduce the Universal Error Corrector with Seasonal-Trend Decomposition (UEC-STD), which significantly improves correction accuracy and robustness across 4 backbones and 10 datasets. Our findings provide a practical tool for enhancing forecasts while offering new insights into mitigating autoregressive errors in deep time-series models. Code is available at https://github.com/DA2I2-SLM/UEC-STD.
Efficient acquisition, storage, and utilization of traffic data are critical challenges in spatio-temporal data management. Most traffic data systems collect and store observations at fixed, coarse-grained temporal intervals to reduce storage and computation costs. However, such coarse-grained data severely limits downstream applications that require predictions at a finer temporal granularity. Collecting and maintaining fine-grained traffic data across all locations and time periods would impose a substantial burden on database storage and preprocessing pipelines. To address this temporal granularity mismatch, we formulate a novel problem: predicting fine-grained future traffic using coarse-grained sampled data. We propose the Spatial-Temporal Refinement Predictor (STRP), a granularity-aware framework for spatio-temporal data systems. STRP integrates two components: Tree Convolution for efficient and interpretable spatial dependency modeling, and Inverse Dilated Convolution for progressive temporal extrapolation. STRP supports two practical prediction settings: window-based and duration-based, to handle different forms of granularity mismatch. Experiments on six benchmark datasets show that STRP significantly outperforms state-of-the-art baselines in both accuracy and efficiency. Our work offers a practical and interpretable approach to managing granularity mismatches in spatio-temporal traffic data systems.
While previous research in multivariate time series forecasting has focused on developing complex holistic models, this work advocates for a shift toward a granular, component-level understanding of their impacts. We propose TSCOMP, the first large-scale benchmark that systematically deconstructs deep forecasting methods into their core, fine-grained components--spanning series preprocessing, encoding strategies, network architectures including specific and large time-series models, and optimization methods. Using constrained orthogonal experimental design and extensive evaluations, we conduct multi-view analyses that reveal component effectiveness across different backbones, data characteristics, and their interactions. Beyond providing insights, this benchmark establishes a fine-grained performance corpus comprising over 20,000 model-dataset evaluations, which supports the learning of automated component selection, enabling zero-shot model construction on new datasets. Our experiments demonstrate that the corpus-driven approach, despite its simplicity, consistently outperforms state-of-the-art methods, validating the soundness of our evaluation design and confirming that systematic component selection surpasses manually designed complex architectures. All code and the performance corpus are publicly available at https://github.com/SUFE-AILAB/TSCOMP.