Compositional Time Series: A Review

AGUILAR, LUCÍA; BARCELÓ VIDAL, CARLES; LARROSA, JUAN M.C.

Lisboa

Congreso; 56th Session of the International Statistical Institute (ISI 2007); 2007

International Statistical Institute

Compositional data are inherently multivariate by nature but are characterized by the distinguishing feature that they are comprised of non-negative components which sum to a constant. Without loss of generality, it can be assumed that the constant in question is 1. More than twenty years have elapsed since Aitchinson's pioneering contributions to the field were published (see Aitchinson (1986) and references therein). These contributions to the literature were seminal in the sense that they were the first publications which developed statistical methods specifically designed for the analysis of compositional data and illustrated their use in the analysis of real compositional data. Nevertheless, a number of earlier studies, primarily involving the use of multivariate methods in the analysis of geological data, had discussed and criticized the application of standard multivariate techniques which ignored the non-negativity and unit-sum constraints inherent in compositional data. Indeed, Pearson, as far back as 1897, had warned of the consequences of using such techniques to explore the correlations between the components making up a composition. Moreover, it is undoubtedly the case that the seminal works of Aitchinson referred to above acted as the catalyst for subsequent developments in the field of the statistical analysis of compositional data. Whilst contributions from other authors wereinitially scarce, research in the ¯eld has, in recent years, exhibited renewed and increasing interest.