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.

翻译：时间序列分解为趋势、季节结构和残差分量是异常检测、变点检测和预测等下游分析的核心基础操作。然而，现有大多数季节-趋势分解方法依赖于用户指定或估计的季节长度，并隐含假设周期性结构稳定。这些假设限制了方法在大型异构数据集中的鲁棒性和可部署性，因为此类数据中的重复模式可能存在漂移、间歇出现或存在于多时间尺度。本文提出LGTD（局部-全局趋势分解），一种无需季节长度的分解框架，将时间序列表示为平滑全局趋势、自适应局部趋势（其重复出现会诱导隐式/涌现的季节结构）以及残差分量的总和。LGTD不通过固定或估计周期来显式建模季节性，而是将季节结构视为重复局部趋势机制涌现的特性。具体而言，LGTD首先估计捕获长期演化的全局趋势，随后应用AutoTrend（一种自适应误差驱动的局部线性趋势推断模块）对去趋势信号进行分割，形成短时分段线性机制。在移除全局和局部趋势后获得残差。通过消除手动指定季节长度的需求，LGTD支持对具有不规则、漂移或弱周期性结构的时间序列实现自动化、低干预的部署。我们分析了计算复杂度，证明在温和条件下LGTD的计算复杂度随序列长度呈线性增长。在合成基准测试上的实验表明，该方法在固定、过渡和可变季节长度设置下均能实现鲁棒且均衡的分解性能，尤其在基于周期的方法失效的场景中表现突出。