Abstract

Motivated by the changing taxa of phytoplankton in a freshwater lake over a 20 year span, we discuss a framework to detect and model shifts in a time series of continuous proportions; that is, a vector of proportions measuring the parts of the whole. By reparameterizing the shape of a Dirichlet distribution, we can model the location and scale separately through generalized linear models. A hidden Markov model allows the coefficients of the generalized linear models to change, thus allowing for the time series to undergo multiple regimes. This framework allows a practitioner to adequately model seasonality, trends, or include covariate information as well as detect change points.