Inference for post-change parameters after sequential CUSUM test under AR(1) model

• Second order biases for the change-point estimation and post-change mean are obtained.
• Corrected normal pivot is developed for constructing more accurate confidence interval for the post-change parameters.
• Comparison between the model-based and the classical CUSUM procedures shows that the model-based CUSUM procedure has smaller average delay detection time and bias for the change-point estimation.

For a sequence of correlated normal random variables following the AR(1) change-point model, the inference problem for the change-point and post-change mean is considered when the residuals are used to form the sequential model-based CUSUM procedure. Higher order biases and corrected pivots are developed to construct confidence intervals. Numerical comparison with the classical CUSUM procedure shows that the model-based CUSUM procedure has smaller average delay detection time and change-point estimation bias. Northern hemisphere average temperature data is used for illustration.