A hyperspherical transformation forecasting model for compositional data

Although Aitchison’s [Aitchison, J., 1986. The Statistical Analysis of Compositional Data, Chapman and Hall, London] method of logratio transformation of compositional data is widely used in various domains, it is limited by the assumption of a strict non-negativity of the components and the requirement of special treatments in practice of the zero components. We propose a dimension-reduction approach through a hyperspherical transformation that is capable of resolving the difficulty in maintaining non-negativity and unit-sum in forecasting compositional data over time. Applying the proposed model to a numerical simulation with a 4D compositional data embedded with zero components and forecasting the three production sectors in the Chinese economy both demonstrate the usefulness and validity of the new approach. 2006 Elsevier B.V. All rights reserved.