An approximate Bayes analysis of ARMA model for Indian GDP growth rate data

Abstract

The paper provides an approximate Bayes analysis of autoregressive moving average (ARMA) model using vague priors for the parameters. The approximation is based on the use of conditional likelihood arising from ARMA model after replacing the unknown values by zeros. A sample based approach, in particular, the Gibbs sampler, is used to find out the posterior inferences for the models under consideration. For numerical illustration, Indian gross domestic product (GDP) data are used after assuring the stationarity of the data by differencing it once. Similarly, the data are also checked for invertibility before going for their actual analysis. The results provide the complete posterior analysis of the entertained models for certain small choices of autoregressive and moving average components. The paper also provides model comparison based on posterior predictive loss criterion to recommend for the most appropriate model from the considered ones. The retrospective short term predictions of the data are provided based on the final recommended model. The results are found satisfactory, in general.

Keywords:

• ARMA model
• GDP growth rate
• conditional likelihood
• Gibbs sampler
• adaptive-rejection sampling
• posterior predictive loss
• retrospective prediction

2010 Mathematics Subject Classification:

• 37M10
• 62C10
• 62M20
• 65C05