Sensitivity to Prior Specification in Bayesian Identification of Autoregressive Time Series Models

In this paper we use the Kullback-Leibler divergence to measure the distance between the posteriors of the autoregressive (AR) model order, aiming to evaluate mathematically the sensitivity of the model identification to different types of priors of the model parameters. In particular, we consider three priors for the AR model coefficients, namely Jeffreys', g, and natural conjugate priors, and three priors for the model order including uniform, arithmetic, and geometric priors. Using a large number of Monte Carlo simulations with various values of the model coefficients, model order, and sample size, we evaluate the impact of the posteriors distance in the accuracy of the model identification. Simulation study results show that the posterior of the model order is sensitive to prior distributions, and the highest accuracy of the model identification is obtained from the posterior resulting from the g-prior. Same results are obtained from the application to real-world time series datasets.