  This paper applies conformal prediction techniques to compute simultaneous
prediction bands and clustering trees for functional data. These tools can be
used to detect outliers and clusters. Both our prediction bands and clustering
trees provide prediction sets for the underlying stochastic process with a
guaranteed finite sample behavior, under no distributional assumptions. The
prediction sets are also informative in that they correspond to the high
density region of the underlying process. While ordinary conformal prediction
has high computational cost for functional data, we use the inductive conformal
predictor, together with several novel choices of conformity scores, to
simplify the computation. Our methods are illustrated on some real data
examples.
