Detecting and estimating changes in dependent functional data

Change point detection in sequences of functional data is examined where the functional observations are dependent. Of particular interest is the case where the change point is an epidemic change (a change occurs and then the observations return to baseline at a later time). The theoretical properties for various tests for at most one change and epidemic changes are derived with a special focus on power analysis. Estimators of the change point location are derived from the test statistics and theoretical properties investigated.