Abstract

Most classical time series methods rely on the assumption of second order stationarity. From climate systems to biomedical signals to astrophysical observations, we increasingly encounter time series that evolve, not abruptly, but slowly over time: time series that are locally stationary. We present a fully Bayesian, nonparametric approach for analysing such time series without relying on restrictive model assumptions. Our method uses a dynamic frequency-domain likelihood approximation to capture how dependence structures evolve across both time and frequency. To flexibly learn this evolution of spectral power, we build on a bivariate Bernstein-Dirichlet process prior. We establish strong theoretical guarantees, including sup-norm posterior consistency and L2 contraction rates. Finally, we demonstrate the potential of this methodology on cutting-edge applications: current ground-based gravitational wave data from LIGO and future gravitational wave data from the LISA space mission, where background noise drifts slowly over time due to a cyclo-stationary Galactic signal and evolving instrument noise.