Projection of time series with periodicity on a sphere

Predicting time series necessitates choosing adequate regressors. For this purpose, prior knowledge of the data is required. By projecting the series on a low-dimensional space, the visualization of the regressors helps to extract relevant information. However, when the series includes some periodicity, the structure of the time series is better projected on a sphere than on an Euclidean space. This paper shows how to project time series regressors on a sphere. A user-defined parameter is introduced in a pairwise distance criterion to control the trade-off between trustworthiness and continuity. Moreover, the theory of optimization on manifolds is used to minimize this criterion on a sphere.