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

Fernanda L. Schumacher (), Larissa A. Matos (), Víctor H. Lachos (), Carlos A. Abanto-Valle () and Luis M. Castro ()
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Fernanda L. Schumacher: The Ohio State University
Larissa A. Matos: Universidade Estadual de Campinas
Víctor H. Lachos: University of Connecticut
Carlos A. Abanto-Valle: Federal University of Rio de Janeiro
Luis M. Castro: Pontificia Universidad Católica de Chile

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 19, 637-660

Abstract: Abstract 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.

Keywords: Autoregressive model; Bayesian approach; beta distribution; censored observations, time series; Primary 62M10; Secondary 62F15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13171-024-00341-1

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