  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 variability "between" and
"within" the functional observations. We then present an augmented fused lasso
procedure to split the projections into multiple regions robustly. These
regions act to isolate each changepoint away from the others so that the
powerful univariate CUSUM statistic can be applied region-wise to identify the
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 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 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.
