Epidemic change tests for the mean of innovations of an AR(1)AR(1) process

We study a first order autoregressive process with the autoregressive coefficient ϕ=1ϕ=1 or |ϕ|<1|ϕ|<1. Our aim is to test whether there is an epidemic type change in the mean of innovations with the statistics based on the observations. We use two equivalent Hölderian test statistics: uniform and dyadic increments statistics. We find the limit under null hypothesis of no change, then we establish consistency conditions under alternative.