Modified procedures for change point monitoring in linear models

Monitoring on-line data to detect change point as early as possible is an important issue. It is shown that the existing CUSUM test is inefficient to quickly give an alarm when change point does not occur at the early stage of monitoring. In this paper we propose a set of new monitoring procedures to detect coefficients and error variance change in linear regression models. Our proposed modification, which uses a bandwidth parameter to change the beginning time of monitoring, can detect change point more quickly even if it occurs after a relative longer monitoring time. Simulations suggest that the modified procedures compared with the CUSUM test have the same null distribution but higher power and shorter average run length. In particular, we illustrate the effectiveness of our procedures by IBM stock data and Thailand/U.S. foreign exchange rate data.