Partially linear beta regression model with autoregressive errors

Guillermo Ferreira (), Jorge Figueroa-Zúñiga and Mário Castro

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2015, vol. 24, issue 4, 752-775

Abstract: This paper is focused on developing a methodology to deal with time series data on the unit interval modeled by a partially linear model with correlated disturbances from a Bayesian perspective. In this context, the linear predictor of the beta regression model incorporates an unknown smooth function with time as an auxiliary covariate and a set of regressors. In addition, an autoregressive dependence structure is proposed for the errors of the model. This formulation can capture the dynamic evolution of curves using both non-stochastic explanatory variables and non-parametric components, allowing an accurate fit with a limited number of parameters. Diagnostic measures are derived from the case-deletion approach and an influence measure based on the Kullback–Leibler divergence is studied and thus, a new method to determine the optimal order of the autoregressive processes through an adaptive procedure using the conditional predictive ordinate statistic is presented. A simulation study is conducted to assess some properties of the Bayesian estimator. Finally, the proposed methodology is illustrated in two real-life applications. Copyright Sociedad de Estadística e Investigación Operativa 2015

Keywords: Autoregressive processes; Bayesian modeling; Beta regression; Partially linear model; 62F15; 62J05 (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:testjl:v:24:y:2015:i:4:p:752-775

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DOI: 10.1007/s11749-015-0433-7

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