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对象值时间序列中的长程依赖度量AI 解读

Object-valued time series, including distributions, covariance matrices, networks, and compositions, lack the linear structure required by conventional autocovariance-based definitions of long memory. We develop an intrinsic framework for defining and estimating long memory in metric spaces of negative type. An isometric embedding yields a centered Hilbert-valued process, and the trace of its lag-covariance operator provides a signed, additive measure of temporal dependence.…

非欧对象值时间序列的周期性量化AI 解读

Non-Euclidean object-valued time series are playing a growing role in modern data analysis, and periodicity is a fundamental characteristic of many time series. However, quantifying periodicity in general non-Euclidean random objects remains largely unexplored. In this work, we introduce a novel nonparametric framework for quantifying periodicity in random objects within a general metric space that lacks Euclidean structure. Our approach formulates periodicity estimation as…

含未知趋势与周期成分的球面嵌入时间序列AI 解读

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…