The projected dynamic linear model for time series on the sphere

Time series on the unit n-sphere arise in many areas, from ecology, to astronomy, to genetics. There are relatively few models for such data, and the ones that exist suffer from several limitations; they are based on insufficiently flexible distributions, they are often difficult to fit, and many of them apply only to the circular case of n=2. We propose a state space model based on the projected normal distribution that can be applied to spherical time series of arbitrary dimension. We describe how to perform fully Bayesian offline inference for this model using an efficient Gibbs sampling algorithm, and we also describe how to perform online inference for streaming data using a Rao-Blackwellized particle filter. In an analysis of wind direction time series, we show that the proposed model can outperform competing models in terms of point, interval, and density forecasting.

time series

circular statistics

Bayesian statistics

particle filtering 

Mid-Level

Computational Statistics

Symposium on Data Science and Statistics (SDSS) 2023