Parameter change tests for ARMA–GARCH models

This paper considers the problem of testing for parameter change in ARMA–GARCH models. For this, we propose score test and residual-based cumulative sum (CUSUM) test and derive their limiting null distributions. According to our simulation study, the score test performs reasonably in testing for both ARMA and GARCH parameter change, but the residual-based CUSUM test is observed to be unsuitable for detecting changes in parameters belonging to ARMA part. The residual-based CUSUM test, however, outperforms the score test in testing for GARCH parameter change. A real data analysis is provided to illustrate the use of the proposed tests.