Greedy Segmentation for a Functional Data Sequence

We present a new approach known as greedy segmentation (GS) to identify multiple changepoints for a functional data sequence. The proposed multiple changepoint detection criterion links detectability with the projection onto a suitably chosen subspace and the changepoint locations. The changepoint estimator identifies the true changepoints for any predetermined number of changepoint candidates, either over-reporting or under-reporting. This theoretical finding supports the proposed GS estimator, which can be efficiently obtained in a greedy manner. The GS estimator’s consistency holds without being restricted to the conventional at most one changepoint condition, and it is robust to the relative positions of the changepoints. Based on the GS estimator, the test statistic’s asymptotic distribution leads to the novel GS algorithm, which identifies the number and locations of changepoints. Using intensive simulation studies, we compare the finite sample performance of the GS approach with other competing methods. We also apply our method to temporal changepoint detection in weather datasets.