Hidden-Markov Models for Time Series of Continuous Proportions with Excess Zeros

Abstract

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, ${\mathcal {ZOIB}}$, are preferred. This manuscript combines ${\mathcal {ZOIB}}$ 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.