Monitoring Structural Changes in Regression with Long Memory Processes

This paper extends the °uctuation monitoring test of Chu et al. (1996) to the regression model involving stationary or nonstationary long memory regressors and errors by proposing two innovative on-line detectors. In spite of the general framework covered by these detectors, their computational cost is extremely mild in that they do not depend on the bootstrap procedure and do not involve the di±cult issues of choosing a kernel function, a bandwidth parameter, or an autoregressive lag length for the long-run variance estimation. Moreover, under suitable regularity conditions and the null hypothesis of no structural change, the asymptotic distributions of these two detectors are identical to that of the corresponding counterpart considered in Chu et al. (1996) where they consider the short memory processes