Detecting changepoints in functional data has become an important problem as
interest in monitory of climatologies and other various processing monitoring
situations has increased, where the data is functional in nature. The observed
data often contains variability in amplitude (y-axis) and phase (x-axis).
If not accounted for properly, incorrect changepoints can be detected, as well
as underlying mean functions at those changes will be incorrect. In this paper,
an elastic functional changepoint method is developed which properly accounts
for these types of variability. Additionally, the method can detect amplitude
and phase changepoints which current methods in the literature do not, as they
focus solely on the amplitude changepoint. This method can easily be
implemented using the functions directly, or to ease the computational burden
can be computed using functional principal component analysis. We apply the
method to both simulated data and real data sets to show its efficiency in
handling data with phase variation with both amplitude and phase changepoints