Test for parameter change in ARIMA models

In this article we consider the problem of testing for parameter changes in ARIMA models based on the cusum test. The proposed test procedure is applicable to testing for the change from stationary models to non stationary models, and vice versa. The idea is to transform the time series via differencing to make the whole time series as a combination of stationary subseries. For this task, we propose a graphical method to identify the right order of differencing. Then the cusum test statistic proposed by Lee et al. (2003) is constructed based the differenced time series. Simulation study and real data analysis are provided for illustration.