**ABSTRACT **

Application of change-point analysis increases as more data sets are collected in a wide variety of fields. Detection of change-point is useful in modeling and prediction of time series, especially, it has a significant impact on forecasting. The critical value of a test is required to conduct that test in detecting change-point. The calculation of the critical values is based on the distributional asymptotics of the test statistics under the null hypothesis. Cumulative sum (CUSUM) test is a popular change-point test in location model. The convergence of the limit distribution of the CUSUM test statistic is rather slow. Antoch and Hušková (2001) suggested that the critical value of the permutation test, a test based on the bootstrap principle, performs better than the asymptotic critical value of CUSUM test in location model. Inspired by them, we consider a change in the mean with i.i.d. errors to evaluate the performance of the bootstrap and the asymptotic critical values of CUSUM test to the simulated and real data. We used the monthly average rainfall in Cumilla, a district in Bangladesh, from 1948 to 2013 as a real data. We also motivated to develop a forecasting model taking into accout of the detected change-point. The result demonstrates that the performance of the bootstrap critical value of CUSUM test is better than the asymptotic one for both the simulated and real data. Moreover, the accuracy of the monthly average rainfall forecasting in Cumilla is improved by considering the valid change-point in modeling.

## Support the magazine and subscribe to the content

This is premium stuff. Subscribe to read the entire article.