|
We develop methodology for detecting relevant changes in functional time series. Instead of testing for exact equality, for example for the equality of the mean functions before and after a potential change point, we propose to test the null hypothesis of no "relevant" deviation. This means that the null hypothesis is formulated in the form that a metric between the mean functions (or other parameters) is smaller than a given threshold. This formulation is motivated by the fact that small discrepancies might not be of importance in many applied situations.
We consider the $L2$-distance (in the Hilbert space framework) and the maximal deviation (in the Banach space framework) between the curves and develop change point tests via self-normalization and multiplier bootstrap, respectively. The results can also be used to construct confidence bands for the functional object (such as the difference between mean or variance functions before or after the change) causing the change. We investigate the asymptotic properties of the test and study their finite sample properties by means of a simulation study and a data example.
|
