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

Cuevas-Tello, J.C., Tino, P., Raychaudhury, S., Yao, X., Harva M.
Pattern Recognition, Vol. 3, Number 43, pp. 1165-1179, 2010.


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 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. We employ an evolutionary algorithm for the (hyper)parameter estimation. 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. 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. 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.