  Data sets comprised of sequences of curves sampled at high frequencies in
time are increasingly common in practice, but they can exhibit complicated
dependence structures that cannot be modelled using common methods of
Functional Data Analysis (FDA). We detail a hierarchical approach which treats
the curves as observations from a hidden Markov model (HMM). The distribution
of each curve is then defined by another fine-scale model which may involve
auto-regression and require data transformations using moving-window summary
statistics or Fourier analysis. This approach is broadly applicable to
sequences of curves exhibiting intricate dependence structures. As a case
study, we use this framework to model the fine-scale kinematic movement of a
northern resident killer whale (Orcinus orca) off the coast of British
Columbia, Canada. Through simulations, we show that our model produces more
interpretable state estimation and more accurate parameter estimates compared
to existing methods.
