  The analysis of a timeseries can provide many new perspectives if it is
accompanied by the assumption that the timeseries is generated from an
underlying dynamical system. For example, statistical properties of the data
can be related to measure theoretic aspects of the dynamics, and one can try to
recreate the dynamics itself. The underlying dynamics could represent a natural
phenomenon or a physical system, where the timeseries represents a sequence of
measurements. In this paper, we present a completely data-driven framework to
identify and model quasiperiodically driven dynamical systems (Q.P.D.) from the
timeseries it generates. Q.P.D. are a special class of systems that are driven
by a periodic source with multiple base frequencies. Such systems abound in
nature, e.g., astronomy and traffic flow. Our framework reconstructs the
dynamics into two components - the driving quasiperiodic source with generating
frequencies; and the driven nonlinear dynamics. We make a combined use of a
kernel-based harmonic analysis, kernel-based interpolation technique, and
Koopman operator theory. Our framework provides accurate reconstructions and
frequency identification for three real-world case studies.
