A Censored Time Series Analysis for Responses on the Unit Interval: An Application to Acid Rain Modeling

In this paper, we propose an autoregressive model for time series in which the variable of interest lies in the unit interval and is subject to certain threshold values below or above which the measurements are not quantifiable. The model includes an independent beta regression (Ferrari and Cribari-Neto, J. Appl. Stat., 31, 799–815 2004) as a special case. A Markov chain Monte Carlo (MCMC) algorithm is tailored to obtain Bayesian posterior distributions of unknown quantities of interest. The likelihood function was used to compute Bayesian model selection measures. We discuss the construction of the proposed model and compare it with alternative models by using simulated data. Finally, we illustrate the use of our proposal by modeling a left-censored weekly series of acid rain data.