LGTD: New Time Series Decomposition Eliminates Season-Length Guesswork, Runs in Linear Time

Time series decomposition into trend, seasonal, and residual components is a bedrock task for anomaly detection, change-point analysis, and forecasting. Classical methods (e.g., STL, X-13ARIMA-SEATS) require a user-specified or estimated season length and assume stable periodic structure. This breaks down in heterogeneous collections where patterns drift, appear intermittently, or operate at multiple nonstationary scales – forcing brittle, per-series tuning that doesn't scale. LGTD (Local-Global Trend Decomposition), introduced by Chotanansub Sophaken and colleagues, attacks this by removing season length dependency entirely.

LGTD represents a time series as the sum of a smooth global trend, adaptive local trends (inferred via an error-driven local linear segmentation procedure), and a residual. Rather than explicit periodic basis functions, seasonality emerges as a property from the recurrence of local trend regimes – meaning decomposition quality is decoupled from any estimated season length. The authors prove the local trend inference terminates in bounded iterations and runs in linear time in series length, independent of any seasonal parameter. Empirically, LGTD is the fastest method across all tested lengths, while baselines degrade super-linearly. On synthetic benchmarks it achieves balanced accuracy across fixed, transitive, and variable season-length regimes; on real-world data it yields interpretable components with low-structure residuals. Code and datasets are available on GitHub.