What is the effect of sample and prior distributions on a Bayesian autoregressive linear model? An application to piped water consumption

Andrés Ramírez Hassan (), Jhonatan Cardona Jiménez () and Raul Pericchi Guerra ()

No 12434, Documentos de Trabajo de Valor Público from Universidad EAFIT

Abstract: In this paper we analyze the effect of four possible alternatives regarding the prior distributions in a linear model with autoregressive errors to predict piped water consumption: Normal-Gamma, Normal-Scaled Beta two, Studentized-Gamma and Student's t-Scaled Beta two. We show the effects of these prior distributions on the posterior distributions under different assumptions associated with the coefficient of variation of prior hyperparameters in a context where there is a conflict between the sample information and the elicited hyperparameters. We show that the posterior parameters are less affected by the prior hyperparameters when the Studentized-Gamma and Student's t-Scaled Beta two models are used. We show that the Normal-Gamma model obtains sensible outcomes in predictions when there is a small sample size. However, this property is lost when the experts overestimate the certainty of their knowledge. In the case that the experts greatly trust their beliefs, it is a good idea to use Student's t distribution as the prior distribution, because we obtain small posterior predictive errors. In addition, we find that the posterior predictive distributions using one of the versions of Student's t as prior are robust to the coefficient of variation of the prior parameters. Finally, it is shown that the Normal-Gamma model has a posterior distribution of the variance concentrated near zero when there is a high level of confidence in the experts' knowledge: this implies a narrow posterior predictive credibility interval, especially using small sample sizes.

Keywords: Autoregressive model; Bayesian analysis; Forecast; Robust prior (search for similar items in EconPapers)
JEL-codes: C11 C53 (search for similar items in EconPapers)
Pages: 32
Date: 2014-07-23
New Economics Papers: this item is included in nep-ecm and nep-for
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Persistent link: https://EconPapers.repec.org/RePEc:col:000122:012434

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