Epidemic change-point detection in general causal time series

We consider an epidemic change-point detection in a large class of causal time series models, including among other processes, AR($\mathrm{\infty }$), ARCH($\mathrm{\infty }$), TARCH($\mathrm{\infty }$), ARMA-GARCH. A test statistic based on the Gaussian quasi-maximum likelihood estimator of the parameter is proposed. It is shown that, under the null hypothesis of no change, the test statistic converges to a distribution obtained from a difference of two Brownian bridge and diverges to infinity under the epidemic alternative. Numerical results for simulation and real data example are provided.