A CUSUM test for a long memory heterogeneous autoregressive model

A CUSUM test is proposed for testing structural breaks in a long-memory heterogeneous autoregressive model. The limiting distribution of the CUSUM test is shown to be a simple function of a standard Brownian bridge, contrasting with the nuisance parameter dependent asymptotics of other CUSUM tests based on fractional integration models. A Monte-Carlo experiment investigates finite sample size and power of the test. The proposed test is applied to a set of daily realized volatilities of the log-return of the Korean Won US Dollar exchange rate to reveal some evidence of a break in addition to a long-memory.