Test for parameter change in ARMA models with GARCH innovations

In this paper, we consider the problem of testing for a parameter change in ARMA models with GARCH innovations. For this purpose, we use the cusum test introduced by Lee et al. [Lee, S., Ha, J., Na, O., Na, S., 2003. The cusum test for parameter change in time series models. Scand. J. Statist. 30, 781-796]. The cusum test statistic is constructed based on the quasi-maximum likelihood estimator. It is shown that the test statistic weakly converges to the sup of the sum of the squares of independent Brownian bridges.