A Bayes algorithm for model compatibility and comparison of ARMA(p,q) models


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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics, Statistics & Probability


ISSN: 1234-7655
eISSN: 2450-0291





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VOLUME 22 , ISSUE 2 (June 2021) > List of articles

A Bayes algorithm for model compatibility and comparison of ARMA(p,q) models

Praveen Kumar Tripathi * / Rijji Sen * / S.K. Upadhyay *

Keywords : ARMA model, exact likelihood, Gibbs sampler, Metropolis algorithm, posterior predictive loss, model compatibility, Ljung-Box-Pierce statistic, GDP growth rate

Citation Information : Statistics in Transition New Series. Volume 22, Issue 2, Pages 95-123, DOI: https://doi.org/10.21307/stattrans-2021-018

License : (CC BY-NC-ND 4.0)

Received Date : 24-October-2017 / Accepted: 16-June-2020 / Published Online: 13-June-2021



The paper presents a Bayes analysis of an autoregressive-moving average model and its components based on exact likelihood and weak priors for the parameters where the priors are defined so that they incorporate stationarity and invertibility restrictions naturally. A GibbsMetropolis hybrid scheme is used to draw posterior-based inferences for the models under consideration. The compatibility of the models with the data is examined using the LjungBox-Pierce chi-square-based statistic. The paper also compares different compatible models through the posterior predictive loss criterion in order to recommend the most appropriate one. For a numerical illustration of the above, data on the Indian gross domestic product growth rate at constant prices are considered. Differencing the data once prior to conducting the analysis ensured their stationarity. Retrospective short-term predictions of the data are provided based on the final recommended model. The considered methodology is expected to offer an easy and precise method for economic data analysis.

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