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-& phi; convergence theory as presented in Feray 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. & COPY; 2023 Elsevier B.V. All rights reserved.