Functional Models and Dynamics

Abstract

This chapter brings us to the study of continuous time dynamics, where functional data analysis has, perhaps, its greatest utility by providing direct access to relationships between derivatives that could otherwise be studied only indirectly. Although dynamic systems are the subject of a large mathematical literature, they are relatively uncommon in statistics. We have therefore devoted the first section of this chapter to reviewing them and their properties. Then we address how “principal differential analysis (PDA)” can contribute to their study from an empirical perspective.