An empirical likelihood-based unified test for the integer-valued AR(1) models

Abstract

In this paper, we suggest an empirical likelihood-based test for the autoregressive coefficient of an integer-valued AR(1) model, i.e., INAR(1). We derive the limit distributions of the resulting test statistic under both null and alternative hypotheses. It turns out that regardless of whether the INAR process is stable or unstable, the statistic is always chi-squared distributed asymptotically under the null hypothesis, and as a result, it can offer unified inferences for the autoregressive coefficient. The performance of its finite sample is also demonstrated using simulations and an empirical example.