Abstract

Motivated by problem of inferring the molecular dynamics of DNA in solution, and linking the dynamics with the base-pair composition, we consider the problem of estimation and comparison of the dynamics of (stationary) time series of curves.

We tackle the problem of estimation and comparison of the dynamics of time series of curves by a frequency domain approach: intuitively, this consists in decomposing the oscillation of the time series of curves into oscillations at distinct frequencies. The frequency-wise fluctuation of the time series, which are contained in the so-called spectral density operator (or spectra), can then be used to compare the dynamics of two time series of curves. In particular, this is applied to comparing the dynamics of two DNA minicircle trajectories (obtained by Molecular Dynamics simulations). We carry out hypothesis tests to compare their spectra, and localize their differences both in frequencies and on the DNA minicircles.