Uncovering delayed patterns in noisy and irregularly sampled time series: An astronomy application

Abstract

We study the problem of estimating the time delay between two signals representing delayed, irregularly sampled and noisy versions of the same underlying pattern. We propose and demonstrate an evolutionary algorithm for the (hyper)parameter estimation of a kernel-based technique in the context of an astronomical problem, namely estimating the time delay between two gravitationally lensed signals from a distant quasar. Mixed types (integer and real) are used to represent variables within the evolutionary algorithm. We test the algorithm on several artificial data sets, and also on real astronomical observations of quasar Q0957+561. By carrying out a statistical analysis of the results we present a detailed comparison of our method with the most popular methods for time delay estimation in astrophysics. Our method yields more accurate and more stable time delay estimates: for Q0957+561, we obtain 419.6 days between images A and B. Our methodology can be readily applied to current state-of-the-art optical monitoring data in astronomy, but can also be applied in other disciplines involving similar time series data.

COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses

“…Hirv et al (2011) provide an overview of the different existing approaches, and present an algorithm based on the optimal prediction technique by Press et al (1992). Recent works focusing on the statistical tools include a Bayesian estimation scheme (Harva & Raychaudhury 2008) and a kernel-based approach combined with an evolutionary algorithm (Cuevas-Tello et al 2010).…”

Computational Intelligence in Astronomy – A Win-Win Situation

“…In [5,4] we introduced a model based technique for estimating time delays in fluxes from gravitationally lensed objects (such as quasars). The main idea of the method was to impose an internal model on the quasar variability in time and then expect that the multiple images will follow that model, up to observational noise and time delays.…”

“…In [4] we generated a large number of flux times series resembling fluxes from real quasars. Three data generation mechanisms were considered:…”

Kernel regression estimates of time delays between gravitationally lensed fluxes

“…Some of the authors of the present work previously proposed a kernel-based method with variable width (K-V) for time delay estimation (Cuevas-Tello, Tiňo & Raychaudhury 2006). This was combined with an evolutionary algorithm (EA) for parameter optimisation (Cuevas-Tello et al 2009). However, the computational time complexity of EA method is O(n 6 ) (Cuevas-Tello 2007).…”