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We proposed a Bayesian analysis for estimating an unknown parameter in a Random Coefficient Autoregressive (RCA) model and its AutoRegressive (AR) process errors. We called this model an RCA model with autocorrelated errors (RCA-AR). A Markov Chain Monte Carlo (MCMC) method was used to generate samples from a posterior distribution which, after having been averaged, gave the estimated value of the unknown parameter. We used a Gibbs sampling algorithm in our MCMC calculation. To compare the performances of the RCA and the RCA-AR models, a simulation was performed with a set of test data and then the mean square errors obtained were used to indicate their performance. The result was that the RCA-AR model worked better than the RCA model in every case. Lastly, we tried both models with real data. They were used to estimate a series of monthly averages of the Stock Exchange of Thailand (SET) index. The result was that the RCA-AR still worked better than the RCA model, similar to the simulation of test data.

Comparing random coefficient autoregressive model with and without autocorrelated errors by Bayesian analysis