On score vector- and residual-based CUSUM tests in ARMA-GARCH models

摘要

In this study, we consider the problem of testing for a parameter change in ARMA-GARCH models. We suggest two types of cumulative sum (CUSUM) tests, namely, score vector- and residual-based CUSUM tests. It is shown that under regularity conditions, their limiting null distributions are the sup of Brownian bridges. A simulation study and real data analysis are conducted for illustration.