A1322
Title: Spherically embedded time series with unknown trend and periodic components
Authors: Han Lin Shang - Macquarie University (Australia)
Jiazhen Xu - Australian National University (Australia) [presenting]
Abstract: Spherically embedded time series are time series with values naturally residing on or can be equivalently mapped to the unit sphere. Despite their ubiquity, these data often exhibit complex non-stationarity driven by latent deterministic 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 modeling and forecasting. To address this methodological gap, a unified geometric framework for the analysis of non-stationary spherically embedded time series is proposed. Central to this approach is a nonparametric spherical trend-periodicity decomposition model, which utilizes an optimal-transport-based removal operator to systematically decouple the deterministic components while preserving the spherical topology. The estimation procedure operates sequentially where the global smooth trend is first estimated and extracted, followed by the identification of the unknown period and the extraction of the periodic structure. The resulting de-trended and de-seasonalized stationary residuals can be further modeled via a spherical autoregressive process. The practical utility of this methodology is validated through applications to U.S. electricity generation compositions and bike trip volume profiles in New York City, yielding significantly enhanced forecasting accuracy while providing interpretable insights into the underlying structural dynamics.
