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( ∞ ), ARCH( TARCH( ARMA-GARCH. A test statistic based on the Gaussian quasi-maximum likelihood estimator parameter is proposed. It shown that, under null hypothesis no change, converges to distribution obtained from difference two Brownian bridge and diverges infinity alternative. Numerical results for simulation real data example are provided.