Fluctuations and precise deviations of cumulative INAR time series

In this paper, we study fluctuations and precise deviations of cumulative INAR time series, both in a non-stationary and in a stationary regime. The theoretical results are based on the recent mod-φ convergence theory as presented in Féray et al., 2016. We apply our findings to the construction of approximate confidence intervals for model parameters and to quantile calculation in a risk management context.