Introduction of General Distributions on Sphere and Torus in View of Time Series Spectra

Abstract

There are various fields where observations are taken on directions in three dimensions, e.g., sphere and torus. Herewe will introduce a very general family of distributions on sphere and torus by use of time series spectra, which includes a lot of proposed classical one as special cases. Because time series spectra can be described by a lot of famous parametric models, e.g., AR, ARMA etc., we can develop the systematic model selection in this field by use of AIC, BIC, etc. Applications are very wide.

Keywords

• distributions on sphere and torus
• time series spectra
• ar, arma models
• model selection