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

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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.

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Acknowledgements

We thank the AE and two anonymous reviewers whose comments and suggestions have substantially improved the paper. Fernanda L. Schumacher acknowledges the partial financial support from CAPES-Brazil. Larissa A. Matos acknowledges support from CNPq-Brazil (307105/2022-9). Victor Lachos acknowledges the partial financial support from UConn - CLAS’s Summer Research Funding Initiative 2023. Carlos A. Abanto-Valle acknowledges partial financial support from Fundação Carlos Chagas Filho de Amparo á Pesquisa do Estado do Rio de Janeiro (FAPERJ). Luis M. Castro acknowledges support from Grant FONDECYT 1220799 from the Chilean government. The authors also thank Guillermo Ferreira for his input in this work.

Funding

CAPES-Brazil, UConn - CLAS’s Summer Research Funding Initiative 2023, CNPq-Brazil 307105/2022-9, Fundação Carlos Chagas Filho de Amparo á Pesquisa do Estado do Rio de Janeiro (FAPERJ), and Grant FONDECYT 1220799 from the Chilean government.

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Authors and Affiliations

  1. College of Public Health, The Ohio State University, Columbus, OH, USA

    Fernanda L. Schumacher

  2. Department of Statistics, Universidade Estadual de Campinas, São Paulo, Brazil

    Larissa A. Matos

  3. Department of Statistics, University of Connecticut, Mansfield, CT, USA

    Víctor H. Lachos

  4. Department of Statistics, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Carlos A. Abanto-Valle

  5. Department of Statistics, Pontificia Universidad Católica de Chile, Santiago, Chile

    Luis M. Castro

  6. Center for the Discovery of Structures in Complex Data, Santiago, Chile

    Luis M. Castro

Authors
  1. Fernanda L. Schumacher
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  2. Larissa A. Matos
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  3. Víctor H. Lachos
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  4. Carlos A. Abanto-Valle
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  5. Luis M. Castro
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Correspondence to Luis M. Castro.

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Schumacher, F.L., Matos, L.A., Lachos, V.H. et al. A Censored Time Series Analysis for Responses on the Unit Interval: An Application to Acid Rain Modeling. Sankhya A 86, 637–660 (2024). https://doi.org/10.1007/s13171-024-00341-1

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