LGTD: Local-Global Trend Decomposition for Season-Length-Free Time Series Analysis

2026-01-08

arXiv.org

AI Summary

This work proposes an adaptive time series decomposition framework that eliminates the need to predefine or estimate seasonal periods, addressing the limitations of traditional methods in handling non-stationary, drifting, or multi-scale seasonal patterns. The approach decomposes a sequence into three components: a global trend, an adaptive local linear trend that implicitly captures seasonality, and a residual. An AutoTrend module dynamically partitions the local trend in an error-driven manner, while global smoothing ensures coherent long-term structure; seasonality emerges automatically as a recurring pattern in the local trends. Operating in linear time, the method demonstrates robust performance across synthetic datasets with fixed, transitioning, and varying seasonal periods, achieving high-quality, low-intervention decomposition even in scenarios where conventional techniques fail.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Time series decomposition into trend, seasonal structure, and residual components is a core primitive for downstream analytics such as anomaly detection, change-point detection, and forecasting. However, most existing seasonal-trend decomposition methods rely on user-specified or estimated season lengths and implicitly assume stable periodic structure. These assumptions limit robustness and deployability in large, heterogeneous collections where recurring patterns may drift, appear intermittently, or exist at multiple time scales. We propose LGTD (Local-Global Trend Decomposition), a season-length-free decomposition framework that represents a time series as the sum of a smooth global trend, adaptive local trends whose recurrence induces implicit (emergent) seasonal structure, and a residual component. Rather than explicitly modeling seasonality through a fixed or estimated period, LGTD treats seasonal structure as an emergent property arising from repeated local trend regimes. Concretely, LGTD first estimates a global trend capturing long-term evolution, then applies AutoTrend, an adaptive error-driven local linear trend inference module, to segment the detrended signal into short-lived piecewise-linear regimes. Residuals are obtained after removing both global and local trends. By eliminating manual season-length specification, LGTD supports automated, low-touch deployment across time series with irregular, drifting, or weakly periodic structure. We analyze computational complexity and show that LGTD scales linearly with series length under mild conditions. Experiments on synthetic benchmarks demonstrate robust and balanced decomposition performance across fixed, transitive, and variable season-length settings, especially where period-based methods degrade.

Problem

• time series decomposition
• seasonality
• trend extraction
• periodic structure
• season-length-free

Innovation

• season-length-free
• local-global trend decomposition
• emergent seasonality
• adaptive trend inference
• time series decomposition