Time-Series Decomposition as a Standalone Task: A Mechanism-Driven Diagnostic Benchmark

We benchmark time series decomposition as a standalone evaluation task. While decomposition outputs are widely used to interpret trend and periodic structure, their quality is often assessed informally, and no unified benchmark exists for comparing component recovery under controlled generative mechanisms. We introduce a synthetic evaluation suite with explicit trend and cycle taxonomies, a unified interface covering representative decomposition families, and complementary metrics capturing distinct error modes (shape, phase, and spectral fidelity). Across stationary periodic regimes, STL-family methods are near-ceiling; under non-stationary periodicity (frequency drift, regime switching), fixed-period priors induce phase degradation, while subspace/time-frequency methods better preserve seasonal consistency (adaptive spectral methods may require tuning). We further extend the benchmark with a downstream scientific-discovery track—symbolic regression on decomposed components—showing that a decompose-then-regress pipeline materially improves recoverability and reduces expression complexity, linking decomposition quality to structure discovery. Code, result exports, and the web leaderboard are publicly available through the Hugging Face dataset and leaderboard Space.

Many time series, such as climate records, tides, energy use, and financial indicators, contain several patterns mixed together. A common first step is to separate the data into a long-term trend, repeating cycles, and leftover irregular variation, so that people can better understand what is happening. However, it has often been unclear how to judge whether a decomposition method has actually separated these patterns well, rather than only producing outputs that look reasonable. This paper introduces a public benchmark for evaluating how accurately different decomposition methods recover trends and cycles under controlled test cases. The benchmark shows where common methods work well, where they fail, and what kinds of assumptions make them suitable for different data patterns. We also show that once a time series is decomposed, it becomes easier to discover simple mathematical formulas that describe its structure, compared with trying to find formulas directly from the mixed raw data. This provides a clearer way to compare decomposition methods and to use them for scientific data analysis.