Hidden-Markov models for time series of continuous proportions with excess zeros

Abstract

International audience ; Bounded time series and time series of continuous proportions are often encountered in statistical modeling. Usually, they are addressed either by a logistic transformation of the data, or by specific probability distributions, such as Beta distribution. Nevertheless, these approaches may become quite tricky when the data show an over-dispersion in 0 and/or 1. In these cases, the zero-and/or-one Beta-inflated distributions, ZOIB, are preferred. This manuscript combines ZOIB distributions with hidden-Markov models and proposes a flexible model, able to capture several regimes controlling the behavior of a time series of continuous proportions. For illustrating the practical interest of the proposed model, several examples on simulated data are given, as well as a case study on historical data, involving the military logistics of the Duchy of Savoy during the XVIth and the XVIIth centuries.