Towards a unified test for the intercept of autoregressive models

It has long been an open problem to provide a unified test for the intercept of autoregressive (AR) models. In this paper, we use the empirical likelihood method to solve this issue. It turns out that the resulting test statistic always converges in distribution to a standard chi-squared distribution under the null hypothesis, whether the AR process is stationary or nonstationary, and with or without an intercept. The asymptotic distribution under the local alternative hypothesis is also derived under some mild conditions. Several simulations as well as a real data example are used to show how well the suggested test performs in terms of size and power on a finite sample.