A kernel-based approach to estimating phase shifts between irregularly sampled time series: An application to gravitational lenses

Abstract

Given two scaled, phase shifted and irregularly sampled noisy realisations of the same process, we attempt to recover the phase shift in this contribution. We suggest a kernel-based method that directly models the underlying process via a linear combination of Gaussian kernels. We apply our method to estimate the phase shift between temporal variations, in the brightness of multiple images of the same distant gravitationally lensed quasar, from irregular but simultaneous observations of all images. In a set of controlled experiments, our method outperforms other state-of-art statistical methods used in astrophysics, in particular in the presence of realistic gaps and Gaussian noise in the data. We apply the method to actual observations (at several optical frequencies) of the doubly imaged quasar Q0957+561. Our estimates at various frequencies are more consistent than those of the currently used methods. © Springer-Verlag Berlin Heidelberg 2006.