Confidence Distributions for the INAR Parameter

ABSTRACT We study the integer autoregressive model of order one with Poisson innovations. Focusing on the autoregressive parameter, we derive the large sample confidence distribution function and the confidence density. We then study the implied prior (the ratio of the confidence density to the likelihood), for which we obtain some approximate results valid near the endpoints of the unit interval. These results, as well as simulation studies, illustrate that the implied prior is not flat. However, we find by simulations and two empirical examples that for moderately large sample sizes, Bayesian credibility regions assuming a flat prior are very close to corresponding frequentist confidence regions.