On Parameter Change Test for ARMA Models with Martingale Difference Errors

摘要

This study considers the CUSUM test for ARMA models with stationary martingale difference errors. CUSUM tests are widely used for detecting abrupt changes in time series models. Although they perform adequately in general, their performance is occasionally unsatisfactory in ARMA models. This motivates us to design a new test that can simultaneously detect the ARMA parameter and variance changes. Its null limiting distribution is derived under regularity conditions. Monte Carlo simulations confirm the validity of the proposed test.