TailedTS: Benchmark Dataset for Heavy-Tailed Time Series Prediction and Periodicity Quantification

TL;DR

TailedTS is a large-scale, heavy-tailed Wikipedia page view dataset designed to evaluate and improve time series forecasting models under extreme distributional conditions, with insights into periodicity and robustness.

Contribution

The paper introduces TailedTS, a novel benchmark dataset capturing heavy-tailed, zero-inflated, and non-Gaussian time series data, along with a periodicity quantification framework and evaluation benchmarks.

Findings

Frequent pages have weaker periodicity than less-viewed pages.

Standard Gaussian estimators perform poorly on high-volume traffic.

Robust loss functions improve forecasting accuracy across traffic scales.

Abstract

We present TailedTS, a large-scale benchmark dataset derived from Wikipedia hourly page view observations throughout 2024, specifically designed to test time series forecasting models under heavy-tailed, zero-inflated, and non-Gaussian conditions. The dataset comprises approximately 24.69 billion data points spanning roughly 3 million unique Wikipedia pages per month, stored in high-efficiency Apache Parquet format. Wikipedia traffic follows a pronounced power-law distribution where roughly 5% of pages account for over 70% of total page views, creating a natural and rigorous testbed for model robustness against extreme volatility that are absent from or underrepresented in existing benchmarks such as M4, M5, and UCI electricity datasets. TailedTS enables several research tasks. First, we introduce a periodicity quantification framework based on sparse autoregression with sparsity and non-negativity constraints, revealing that frequently-viewed pages exhibit significantly weaker periodic structure than their less-viewed counterparts, showing direct implications for server allocation and traffic forecasting on large digital platforms. Second, we provide standardized prediction benchmarks evaluated under a suite of non-Gaussian loss functions, including $\ell_1$-norm, Huber, quantile, and $\ell_p$-norm losses, demonstrating that standard Gaussian-based estimators degrade substantially on high-volume page categories, while robust alternatives provide consistent gains across all traffic scales. TailedTS is publicly available at https://doi.org/10.5281/zenodo.17070469.