Scalable Multiple Changepoint Detection for Functional Data Sequences

We propose the Multiple Changepoint Isolation (MCI) method for detecting multiple changes in the mean and covariance of a functional process. We first introduce a pair of projections to represent the high and low frequency features of the data. We then apply total variation denoising and introduce a new regionalization procedure to split the projections into multiple regions. Denoising and regionalizing act to isolate each changepoint into its own region, so that the classical univariate CUSUM statistic can be applied region-wise to find all changepoints. Simulations show that our method accurately detects the number and locations of changepoints under many different scenarios. These include light and heavy tailed data, data with symmetric and skewed distributions, sparsely and densely sampled changepoints, and both mean and covariance changes. We show that our method outperforms a recent multiple functional changepoint detector and several univariate changepoint detectors applied to our proposed projections. We also show that the MCI is more robust than existing approaches, and scales linearly with sample size. Finally, we demonstrate our method on a large time series of water vapor mixing ratio profiles from atmospheric emitted radiance interferometer measurements.