Journal
TEST
Volume 24, Issue 4, Pages 752-775Publisher
SPRINGER
DOI: 10.1007/s11749-015-0433-7
Keywords
Autoregressive processes; Bayesian modeling; Beta regression; Partially linear model
Categories
Funding
- CONICYT, Chile
- DIUC [213.014.021-1.0]
- FONDECYT from the Chilean government [11130483]
- CNPq, Brasil
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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.
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