Spherically Embedded Time Series with Unknown Trend and Periodic Components
含未知趋势与周期成分的球面嵌入时间序列AI 解读 ↓
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含未知趋势与周期成分的球面嵌入时间序列
- 研究问题
- 当时间序列取值位于球面且存在未知趋势与周期时，如何保留非欧几何结构进行分解、建模与预测？
- 方法与思路
- 作者以最优传输移除操作依次提取非参数趋势与周期，再用球面自回归模型刻画去趋势、去季节后的残差。
- 材料陈述的贡献
- 摘要称建立时间依赖下的一致性理论，并在模拟、电力构成及骑行量轮廓应用中报告较好的有限样本预测表现。
- 阅读关注点
- 核对球面映射、移除操作与分解的定义，残差平稳性及一致性条件，并检查预测比较的基准和评价方案。
- 阅读边界
- 这是 arXiv 预印本，同行评审及接收未核实；摘要未说明具体正则条件或预测改善数值，不能确认普遍优越性。
原文摘要
Spherically embedded time series are time series with values naturally residing on or can be equivalently mapped to the sphere. Despite their ubiquity in diverse scientific fields, these data frequently exhibit complex non-stationarity driven by latent trend and periodic components. Traditional Euclidean time series methods fail to account for the intrinsic non-Euclidean geometry of the sphere, leaving a critical gap in rigorous methodologies for modelling and forecasting nonstationary spherically embedded time series. To address this methodological gap, we propose a unified geometric framework to analyse nonstationary spherically embedded time series. Central to our approach is a novel nonparametric spherical trend-periodicity decomposition model that uses an optimal-transport-based removal operation to sequentially extract the smooth trend and periodic components while preserving spherical topology. The resulting de-trended and de-seasonalised stationary residuals can be further modelled using a spherical autoregressive model, formalising a novel trend-periodic spherical autoregressive model. Theoretical foundations for the modelling procedure are established on the consistency under temporal dependence. Extensive simulations corroborate these theoretical guarantees and demonstrate the superior finite-sample predictive performance of the trend-periodic spherical autoregressive model. Finally, we validate the practical utility of our methodology through applications to electricity generation compositions and bike trip volume profiles, yielding significantly enhanced forecasting accuracy while providing interpretable insights into the underlying structural dynamics.